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  • Articles  (213)
  • linear programming  (146)
  • mercury
  • Mathematics  (143)
  • Energy, Environment Protection, Nuclear Power Engineering  (67)
  • Electrical Engineering, Measurement and Control Technology  (3)
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  • Articles  (213)
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  • 1
    Electronic Resource
    Electronic Resource
    Mercury and selenium in arctic and coastal seals off the coast of Norway
    Amsterdam : Elsevier
    Environmental Pollution 85 (1994), S. 153-160 
    Details
    ISSN: 0269-7491
    Keywords: grey seal ; harbour seal ; harp seal ; mercury ; ringed seal ; selenium
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0269-7491(94)90081-7
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  • 2
    Electronic Resource
    Electronic Resource
    Influence of Prenatal Mercury Exposure Upon Scholastic and Psychological Test Performance: Benchmark Analysis of a New Zealand Cohort (1998)
    Springer
    Risk analysis 18 (1998), S. 701-713 
    Details
    ISSN: 1539-6924
    Keywords: Benchmark ; mercury ; risk assessment ; epidemiology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This paper presents benchmark (BMD) calculations and additional regression analyses of data from a study in which scores from 26 scholastic and psychological tests administered to 237 6- and 7-year-old New Zealand children were correlated with the mercury concentration in their mothers' hair during pregnancy. The original analyses of five test scores found an association between high prenatal mercury exposure and decreased test performance, using category variables for mercury exposure. Our regression analyses, which utilized the actual hair mercury level, did not find significant associations between mercury and children's test scores. However, this finding was highly influenced by a single child whose mother's mercury hair level (86 mg/kg) was more than four times that of any other mother. When that child was omitted, results were more indicative of a mercury effect and scores on six tests were significantly associated with the mothers' hair mercury level. BMDs calculated from five tests ranged from 32 to 73 mg/kg hair mercury, and corresponding BMDLs (95% lower limits on BMDs) ranged from 17 to 24 mg/kg. When the child with the highest mercury level was omitted, BMDs ranged from 13 to 21 mg/kg, and corresponding BMDLs ranged from 7.4 to 10 mg/kg.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/B:RIAN.0000005917.52151.e6
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  • 3
    Electronic Resource
    Electronic Resource
    On multilevel iterative methods for optimization problems (1990)
    Springer
    Mathematical programming 48 (1990), S. 1-17 
    Details
    ISSN: 1436-4646
    Keywords: Coercivity ; quadratic programming ; linear programming ; aggregation ; relaxation ; multigrid methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper is concerned with multilevel iterative methods which combine a descent scheme with a hierarchy of auxiliary problems in lower dimensional subspaces. The construction of auxiliary problems as well as applications to elasto-plastic model and linear programming are described. The auxiliary problem for the dual of a perturbed linear program is interpreted as a dual of perturbed aggregated linear program. Coercivity of the objective function over the feasible set is sufficient for the boundedness of the iterates. Equivalents of this condition are presented in special cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582249
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  • 4
    Electronic Resource
    Electronic Resource
    Making sparse matrices sparser: Computational results (1990)
    Springer
    Mathematical programming 49 (1990), S. 91-111 
    Details
    ISSN: 1436-4646
    Keywords: Sparse matrices ; linear programming ; bipartite matching
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Many optimization algorithms involve repeated processing of a fixed set of linear constraints. If we pre-process the constraint matrixA to be sparser, then algebraic operations onA will become faster. We consider the problem of making a given matrix as sparse as possible, theSparsity Problem (SP). In a companion paper with S. Frank Chang, we developed some theoretical algorithms for SP under a non-degeneracy assumption (McCormick and Chang, 1988). Here we investigate what must be done to make those algorithms applicable in practice. We report encouraging computational results in making linear programming constraint matrices sparser. We also find that the Simplex Algorithm can solve the reduced LPs faster. Comparisons are made to a heuristic algorithm for SP of Adler et al. (1989).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588780
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  • 5
    Electronic Resource
    Electronic Resource
    Limiting behavior of the affine scaling continuous trajectories for linear programming problems (1991)
    Springer
    Mathematical programming 50 (1991), S. 29-51 
    Details
    ISSN: 1436-4646
    Keywords: Interior-point methods ; linear programming ; Karmarkar's algorithm ; logarithmic barrier function ; affine scaling algorithms ; continuous trajectories for linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the continuous trajectories of the vector field induced by the primal affine scaling algorithm as applied to linear programming problems in standard form. By characterizing these trajectories as solutions of certain parametrized logarithmic barrier families of problems, we show that these trajectories tend to an optimal solution which in general depends on the starting point. By considering the trajectories that arise from the Lagrangian multipliers of the above mentioned logarithmic barrier families of problems, we show that the trajectories of the dual estimates associated with the affine scaling trajectories converge to the so called ‘centered’ optimal solution of the dual problem. We also present results related to asymptotic direction of the affine scaling trajectories. We briefly discuss how to apply our results to linear programs formulated in formats different from the standard form. Finally, we extend the results to the primal-dual affine scaling algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01594923
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  • 6
    Electronic Resource
    Electronic Resource
    On the convergence of the exponential multiplier method for convex programming (1993)
    Springer
    Mathematical programming 60 (1993), S. 1-19 
    Details
    ISSN: 1436-4646
    Keywords: Convex programming ; linear programming ; multiplier method ; exponential penalty ; Augmented Lagrangian
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy “proximal” term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580598
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  • 7
    Electronic Resource
    Electronic Resource
    Use of dynamic trees in a network simplex algorithm for the maximum flow problem (1991)
    Springer
    Mathematical programming 50 (1991), S. 277-290 
    Details
    ISSN: 1436-4646
    Keywords: Algorithms ; complexity ; data structures ; dynamic trees ; graphs ; linear programming ; maximum flow ; network flow ; network optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n 2 m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01594940
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  • 8
    Electronic Resource
    Electronic Resource
    Series parallel composition of greedy linear programming problems (1993)
    Springer
    Mathematical programming 62 (1993), S. 1-14 
    Details
    ISSN: 1436-4646
    Keywords: Greedy algorithm ; Monge arrays ; series parallel graphs ; linear programming ; network flow ; transportation problem ; integrality ; convexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We study the concept of series and parallel composition of linear programming problems and show that greedy properties are inherited by such compositions. Our results are inspired by earlier work on compositions of flow problems. We make use of certain Monge properties as well as convexity properties which support the greedy method in other contexts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585157
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  • 9
    Electronic Resource
    Electronic Resource
    On lower bound updates in primal potential reduction methods for linear programming (1991)
    Springer
    Mathematical programming 52 (1991), S. 415-428 
    Details
    ISSN: 1436-4646
    Keywords: Interior point methods ; linear programming ; potential reduction methods ; Karmarkar's algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a procedure for computing lower bounds for the optimal cost in a linear programming problem. Whenever the procedure succeeds, it finds a dual feasible slack and the associated duality gap. Although no projective transformations or problem restatements are used, the method coincides with the procedures by Todd and Burrell and by de Ghellinck and Vial when these procedures are applicable. The procedure applies directly to affine potential reduction algorithms, and improves on existent techniques for finding lower bounds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582898
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  • 10
    Electronic Resource
    Electronic Resource
    An interior point potential reduction algorithm for the linear complementarity problem (1992)
    Springer
    Mathematical programming 54 (1992), S. 267-279 
    Details
    ISSN: 1436-4646
    Keywords: Linear complementarity ; P-matrix ; interior point ; potential function ; linear programming ; quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The linear complementarity problem (LCP) can be viewed as the problem of minimizingx T y subject toy=Mx+q andx, y⩾0. We are interested in finding a point withx T y 〈ε for a givenε 〉 0. The algorithm proceeds by iteratively reducing the potential function $$f(x,y) = \rho \ln x^T y - \Sigma \ln x_j y_j ,$$ where, for example,ρ=2n. The direction of movement in the original space can be viewed as follows. First, apply alinear scaling transformation to make the coordinates of the current point all equal to 1. Take a gradient step in the transformed space using the gradient of the transformed potential function, where the step size is either predetermined by the algorithm or decided by line search to minimize the value of the potential. Finally, map the point back to the original space. A bound on the worst-case performance of the algorithm depends on the parameterλ *=λ*(M, ε), which is defined as the minimum of the smallest eigenvalue of a matrix of the form $$(I + Y^{ - 1} MX)(I + M^T Y^{ - 2} MX)^{ - 1} (I + XM^T Y^{ - 1} )$$ whereX andY vary over the nonnegative diagonal matrices such thate T XYe ⩾ε andX jj Y jj⩽n 2. IfM is a P-matrix,λ * is positive and the algorithm solves the problem in polynomial time in terms of the input size, |log ε|, and 1/λ *. It is also shown that whenM is positive semi-definite, the choice ofρ = 2n+ $$\sqrt {2n} $$ yields a polynomial-time algorithm. This covers the convex quadratic minimization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586054
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  • 11
    Electronic Resource
    Electronic Resource
    A polynomial method of approximate centers for linear programming (1992)
    Springer
    Mathematical programming 54 (1992), S. 295-305 
    Details
    ISSN: 1436-4646
    Keywords: Interior-point method ; linear programming ; Karmarkar's method ; polynomial-time algorithm ; logarithmic barrier function ; path-following method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a path-following algorithm for the linear programming problem with a surprisingly simple and elegant proof of its polynomial behaviour. This is done both for the problem in standard form and for its dual problem. We also discuss some implementation strategies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586056
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  • 12
    Electronic Resource
    Electronic Resource
    A globally and quadratically convergent affine scaling method for linearℓ 1 problems (1992)
    Springer
    Mathematical programming 56 (1992), S. 189-222 
    Details
    ISSN: 1436-4646
    Keywords: 65H10 ; 65K05 ; 65K10 ; Linearℓ 1 estimation ; linear programming ; interior-point algorithm ; simplex method ; least absolute value regression ; affine scaling method ; Karmarkar
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Recently, various interior point algorithms related to the Karmarkar algorithm have been developed for linear programming. In this paper, we first show how this “interior point” philosophy can be adapted to the linear ℓ1 problem (in which there are no feasibility constraints) to yield a globally and linearly convergent algorithm. We then show that the linear algorithm can be modified to provide aglobally and ultimatelyquadratically convergent algorithm. This modified algorithm appears to be significantly more efficient in practise than a more straightforward interior point approach via a linear programming formulation: we present numerical results to support this claim.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580899
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  • 13
    Electronic Resource
    Electronic Resource
    On the finite convergence of interior-point algorithms for linear programming (1992)
    Springer
    Mathematical programming 57 (1992), S. 325-335 
    Details
    ISSN: 1436-4646
    Keywords: Strict complementarity ; interior point algorithms ; linear programming ; optimal face
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It has been shown [8] that numerous interior-point algorithms for linear programming (LP) generate solution sequences that converge to strict complementarity solutions, or interior solutions on the optimal face. In this note we further establish a theoretical base for Gay's test (Gay, 1989) to identify the optimal face, and develop a new termination procedure to obtain an exact solution on the optimal face. We also report some numerical results for solving a set of LP test problems, each of which has a highly degenerate and unbounded optimal face.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581087
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  • 14
    Electronic Resource
    Electronic Resource
    Workload planning in small lot printed circuit board assembly (1997)
    Springer
    OR spectrum 19 (1997), S. 147-157 
    Details
    ISSN: 1436-6304
    Keywords: Key words: production ; scheduling ; printed circuit board assembly ; modelling ; linear programming ; aggregational error ; decision support ; Schlüsselwörter: Produktion ; Ablaufplanung ; Leiterplattenbestückung ; Modellierung ; lineare Programmierung ; Aggregationsfehler ; Entscheidungsunterstützung ; S′jm = Sjm ; SFj(r)(12)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. Bei der Kleinserienmontage von Leiterplatten besteht das Problem der Einlastungsplanung darin, ein Tagesprogramm an Produktionsaufträgen zusammenzustellen, die gemeinsam in das Produktionssystem eingeschleust werden. Jeder Produktionsauftrag entspricht einem bestimmten Leiterplattentyp. Wechselt man bei der automatischen Bestückung von Leiterplatten zu einem neuen Leiterplattentyp, so fallen erhebliche Rüstzeiten an, die davon abhängen, wie viele Bauteilezuführungen im Magazin der Bestückungsautomaten ausgewechselt werden müssen. Zur Unterstützung dieses Entscheidungsproblems werden zwei unterschiedliche Modelle der linearen Optimierung entwickelt. Die beiden Modelle unterscheiden sich vor allem durch ihren Aggregationsgrad und ihren Rechenaufwand. Zur Verringerung des Aggregationsfehlers wird ein auf der Fuzzy-Set-Theorie beruhender Ansatz zur Abschätzung der bei automatischen SMD-Bestückungsautomanten auftretenden Rüstzeiten entwickelt. Hierbei wird als industrielles Anwendungsbeispiel die Leiterplattenbestückung in einem bedeutenden Elektronikunternehmen betrachtet. Die durchgeführte numerische Untersuchung zeigt, daß das hochaggregierte Fuzzy-LP-Modell zu hinreichend genauen Lösungen führt und erheblich geringeren Rechenaufwand verursacht als ein detaillierteres LP-Modell. Außerdem wird die praktische Eignung des Fuzzy-LP-Modells für den Einsatz innerhalb eines interaktiven Entscheidungsunterstützungssystems verdeutlicht.
    Notes: Abstract. The problem of workload planning in small lot printed circuit board (PCB) assembly concerns the determination of the daily mix of production orders to be released into the production system. When switching from one production order (board type) to another, a considerable set-up time is incurred based on the number of component feeders to be replaced in the component magazine of the assembly machines. To support the order-mix decision faced by a major electronics manufacturer, two versions of a linear programming model are developed. The models differ primarily in their degree of aggregation and their computational effort. In order to reduce the aggregational error incurred, a fuzzy approach is developed to estimate the number of component set-ups at automatic SMD placement machines. Our numerical investigation reveals that sufficiently accurate solutions may be obtained from a highly aggregate fuzzy LP-model and this is achieved with considerably less computational effort than with a more detailed LP-model. We also demonstrate the potential suitability of the fuzzy LP-model for implementation within an interactive decision support system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01545517
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  • 15
    Electronic Resource
    Electronic Resource
    Workload planning in small lot printed circuit board assembly (1997)
    Springer
    OR spectrum 19 (1997), S. 147-157 
    Details
    ISSN: 1436-6304
    Keywords: production ; scheduling ; printed circuit board assembly ; modelling ; linear programming ; aggregational error ; decision support ; Produktion ; Ablaufplanung ; Leiterplattenbestückung ; Modellierung ; lineare Programmierung ; Aggregationsfehler ; Entscheidungsunterstützung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Bei der Kleinserienmontage von Leiterplatten besteht das Problem der Einlastungsplanung darin, ein Tagesprogramm an Produktionsaufträgen zusammenzustellen, die gemeinsam in das Produktionssystem eingeschleust werden. Jeder Produktionsauftrag entspricht einem bestimmten Leiterplattentyp. Wechselt man bei der automatischen Bestückung von Leiterplatten zu einem neuen Leiterplattentyp, so fallen erhebliche Rüstzeiten an, die davon abhängen, wie viele Bauteilezuführungen im Magazin der Bestückungsautomaten ausgewechselt werden müssen. Zur Unterstützung dieses Entscheidungsproblems werden zwei unterschiedliche Modelle der linearen Optimierung entwickelt. Die beiden Modelle unterscheiden sich vor allem durch ihren Aggregationsgrad und ihren Rechenaufwand. Zur Verringerung des Aggregationsfehlers wird ein auf der Fuzzy-Set-Theorie beruhender Ansatz zur Abschätzung der bei automatischen SMD-Bestückungsautomanten auftretenden Rüstzeiten entwickelt. Hierbei wird als industrielles Anwendungsbeispiel die Leiterplattenbestückung in einem bedeutenden Elektronikunternehmen betrachtet. Die durchgeführte numerische Untersuchung zeigt, daß das hochaggregierte Fuzzy-LP-Modell zu hinreichend genauen Lösungen führt und erheblich geringeren Rechenaufwand verursacht als ein detaillierteres LP-Modell. Außerdem wird die praktische Eignung des Fuzzy-LP-Modells für den Einsatz innerhalb eines interaktiven Entscheidungsunterstützungssystems verdeutlicht.
    Notes: Abstract The problem of workload planning in small lot printed circuit board (PCB) assembly concerns the determination of the daily mix of production orders to be released into the production system. When switching from one production order (board type) to another, a considerable set-up time is incurred based on the number of component feeders to be replaced in the component magazine of the assembly machines. To support the order-mix decision faced by a major electronics manufacturer, two versions of a linear programming model are developed. The models differ primarily in their degree of aggregation and their computational effort. In order to reduce the aggregational error incurred, a fuzzy approach is developed to estimate the number of component set-ups at automatic SMD placement machines. Our numerical investigation reveals that sufficiently accurate solutions may be obtained from a highly aggregate fuzzy LP-model and this is achieved with considerably less computational effort than with a more detailed LP-model. We also demonstrate the potential suitability of the fuzzy LP-model for implementation within an interactive decision support system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01545517
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  • 16
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    Separable Markovian decision problems (1992)
    Springer
    OR spectrum 14 (1992), S. 43-52 
    Details
    ISSN: 1436-6304
    Keywords: Markov decision processes ; linear programming ; Markovsche Entscheidungsprozesse ; lineare Programmierung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Separabele Markoffsche Entscheidungsprobleme haben die Eigenschaft, daß für gewisse Paare (i, a) von Zuständeni und zugehörigen Aktionena gilt: (i) die unmittelbare Auszahlung ist die Summe zweier Terme, von denen der eine nur vom Zustand und der andere nur von der Aktion abhängt (ria=si+ta), (ii) die Übergangswahrscheinlichkeiten hängen nur von der Aktion ab und nicht vom Zustand, in dem diese Aktion gewählt wurde. Dieses Modell wurde schon gegen Ende der Sechziger Jahre untersucht. Es wurde bewiesen, daß diskontierte Probleme und undiskontierte Probleme mit nur einer rekurrenten Klasse als lineare Programme mit weniger Variablen als im allgemeinen Modell formuliert werden können. Es war bisher unbekannt, ob auch für undiskontierte Modelle mit mehreren rekurrenten Klassen eine Formulierung mit weniger Variablen existiert. Dieses Problem wird in der vorliegenden Arbeit gelöst: eine solche Formulierung ist möglich. Abschließend werden einige Anwendungen von separablen Modellen angegeben.
    Notes: Summary Separable Markovian decision problems have the property that for certain pairs (i, a) of a statei and an actiona: (i) the immediate reward is the sum of terms due to the current state and action (ria=Si+ta), (ii) the transition probability depends only on the action and not on the state from which the transition occurs. The separable model was studied already in the late sixties. For the discounted case and the unichain undiscounted case a reduced LP formulation was given, which involves a substantially smaller number of variables than in the LP formulation of a general Markov decision problem. It was unknown whether such an efficient formulation was also possible in the multichain case. This paper solves this problem: such an efficient formulation can be obtained. Some applications of separable models are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01783501
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  • 17
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    Methodical support for elaborating emission reduction strategies (1995)
    Springer
    OR spectrum 17 (1995), S. 41-50 
    Details
    ISSN: 1436-6304
    Keywords: Energy-Emission Modelling ; linear programming ; international environmental policy ; emission reduction strategies ; Energie-Emissions-Modellierung ; lineare Programmierung ; internationale Umweltpolitik ; sionsminderungsstrategien
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Diese Arbeit gibt einen Überblick über methodische Ansätze zur Herleitung nationaler und internationaler Emissionsminderungsstrategien. Zu diesem Zweck werden häufig sogenannte integrierte Energie-Emissions-Modelle (lineare Programme) eingesetzt. Das EG-EFOM-ENV Modell wird vorgestellt und seine prinzipielle Anwendung aufgezeigt. Konkrete Ergebnisse werden anhand des Beispiels Litauens angegeben. Einschränkungen der verwendeten Methodik sowie deren mögliche Erweiterungen werden diskutiert.
    Notes: Abstract This paper provides an insight into the elaboration of strategies for emission reduction at present internationally requested by applying energy-emission models. One of these models, the EC-EFOM-ENV LP-model is presented in detail. Its application is shown in principle as well as to the special situation of countries in transition from a centrally planned to a market economy. The limitations of this approach and further applications on an international level are assessed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01719732
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  • 18
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    Heuristics for the integer one-dimensional cutting stock problem: A computational study (1996)
    Springer
    OR spectrum 18 (1996), S. 131-144 
    Details
    ISSN: 1436-6304
    Keywords: Cutting stock ; integer solutions ; heuristics ; linear programming ; column generation ; numerical experiments ; Zuschneideprobleme ; Ganzzahligkeit ; Heuristiken ; Lineare Optimierung ; Spaltengenerierung ; Numerische Experimente
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In der vorliegenden Arbeit betrachten wir das Problem der Bestimmung ganzzahliger Lösungen für das Standardproblem der eindimensionalen Zuschnittplanung. Insbesondere werden eine spezielle Klasse heuristischer Lösungsverfahren, die in der Literatur beschrieben sind, sowie einige naheliegende Varianten dieser Verfahren vorgestellt. Auf der Grundlage eines numerischen Experiments, bei dem 4.000 Probleme zufällig erzeugt und gelöst wurden, werden die Verfahren miteinander verglichen und im Hinblick auf die Kriterien „Lösungsqualität“ und „Rechenzeitbedarf“ beurteilt. Dabei zeigt sich nicht nur, daß zwei Verfahren deutlich besser als die übrigen einzustufen sind, sondern auch, daß mit ihrer Hilfe nahezu jede Problemausprägung des klassischen eindimensionalen Zuschneideproblems optimal gelöst werden kann.
    Notes: Abstract In this paper the problem of generating integer solutions to the standard one-dimensional cutting stock problem is treated. In particular, we study a specific class of heuristic approaches that have been proposed in the literature, and some straightforward variants. These methods are compared with respect to solution quality and computing time. Our evaluation is based on having solved 4,000 randomly generated test problems. Not only will it be shown that two methods are clearly superior to the others but also that they solve almost any instance of the standard one-dimensional cutting stock problem to an optimum.
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    URL: http://dx.doi.org/10.1007/BF01539705
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  • 19
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    Deckung des Klassenraumbedarfs an Hamburger Schulen (1997)
    Springer
    OR spectrum 19 (1997), S. 67-74 
    Details
    ISSN: 1436-6304
    Keywords: Deckung des Bedarfs an Klassenräumen ; lineare Optimierung ; gemischt ganzzahlige Optimierung ; Covering classroom requirements ; linear programming ; mixed integer programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Abstract The city of Hamburg expects for the next years enormously increasing rates of pupils. Covering the additional need of classrooms by new building is very expensive. It would be better to avoid this by making good use of the existing resources. The possible steps for covering the requirements and the restrictions are explained subsequently. There are a lot of alternatives, which must be coordinated for a “good” solution in a suitable way. The mathematical model for this problem is described furthermore. The model in question belongs to the class of mixed integer problems. Finally the standard optimization software SCICONIC, which is used for solving the mixed integer problem, is introduced and the embedding of SCICONIC into the architecture of the evolved planning system is described. Because the users of the system are officers without knowledge in electronic data processing and mathematical programming, a user friendly interface is of special importance in this case. This paper does not include new mathematical cognition, but describes the skilled use of known OR-techniques in a real software project.
    Notes: Zusammenfassung Die Stadt Hamburg sieht in den nächsten Jahren eine beträchtliche Schülerwelle auf sich zukommen. Daraus resultiert zusätzlicher Klassenraumbedarf, der durch Neubau nur sehr kostspielig gedeckt werden kann. Durch systematische Ausnutzung von bestehenden Raumreserven lassen sich teure Neubaumaßnahmen weitgehend vermeiden. Im folgenden werden zunächst die möglichen Maßnahmen zur Raumbedarfsdeckung mit ihren einschränkenden Bedingungen aufgezeigt. Die Maßnahmen erlauben eine Vielzahl von Handlungsalternativen, die zum wirksamen Einsatz optimal aufeinander abgestimmt werden müssen. Das mathematische Modell zur Lösung dieses Problems wird in der weiteren Folge beschrieben. Es handelt sich um ein gemischt ganzzahliges Optimierungsproblem. Abschließend wird die zur Lösung eingesetzte Standard-Optimierungs-Software SCICONIC vorgestellt und die Einbindung von SCICONIC in das entwickelte Raumplanungssystem geschildert. Da die Anwender des Systems Sachbearbeiter ohne DV- und OR-Erfahrung sind, hat hier Benutzerfreundlichkeit eine besonders hohe Bedeutung. Der vorliegende Aufsatz erhebt nicht den Anspruch auf neue mathematische Erkenntnisse, sondern er beschreibt die fachgerechte Anwendung bekannter OR-Verfahren in einem Software-Projekt der Praxis.
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    Deckung des Klassenraumbedarfs an Hamburger Schulen (1997)
    Springer
    OR spectrum 19 (1997), S. 67-74 
    Details
    ISSN: 1436-6304
    Keywords: Schlüsselwörter: Deckung des Bedarfs an Klassenräumen ; lineare Optimierung ; gemischt ganzzahlige Optimierung ; Key words: Covering classroom requirements ; linear programming ; mixed integer programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Abstract. The city of Hamburg expects for the next years enormously increasing rates of pupils. Covering the additional need of classrooms by new building is very expensive. It would be better to avoid this by making good use of the existing resources. The possible steps for covering the requirements and the restrictions are explained subsequently. There are a lot of alternatives, which must be coordinated for a ``good'' solution in a suitable way. The mathematical model for this problem is described furthermore. The model in question belongs to the class of mixed integer problems. Finally the standard optimization software SCICONIC, which is used for solving the mixed integer problem, is introduced and the embedding of SCICONIC into the architecture of the evolved planning system is described. Because the users of the system are officers without knowledge in electronic data processing and mathematical programming, a user friendly interface is of special importance in this case. This paper does not include new mathematical cognition, but describes the skilled use of known OR-techniques in a real software project.
    Notes: Zusammenfassung. Die Stadt Hamburg sieht in den nächsten Jahren eine beträchtliche Schülerwelle auf sich zukommen. Daraus resultiert zusätzlicher Klassenraumbedarf, der durch Neubau nur sehr kostspielig gedeckt werden kann. Durch systematische Ausnutzung von bestehenden Raumreserven lassen sich teure Neubaumaßnahmen weitgehend vermeiden. Im folgenden werden zunächst die möglichen Maßnahmen zur Raumbedarfsdeckung mit ihren einschränkenden Bedingungen aufgezeigt. Die Maßnahmen erlauben eine Vielzahl von Handlungsalternativen, die zum wirksamen Einsatz optimal aufeinander abgestimmt werden müssen. Das mathematische Modell zur Lösung dieses Problems wird in der weiteren Folge beschrieben. Es handelt sich um ein gemischt ganzzahliges Optimierungsproblem. Abschließend wird die zur Lösung eingesetzte Standard-Optimierungs-Software SCICONIC vorgestellt und die Einbindung von SCICONIC in das entwickelte Raumplanungssystem geschildert. Da die Anwender des Systems Sachbearbeiter ohne DV- und OR-Erfahrung sind, hat hier Benutzerfreundlichkeit eine besonders hohe Bedeutung. Der vorliegende Aufsatz erhebt nicht den Anspruch auf neue mathematische Erkenntnisse, sondern er beschreibt die fachgerechte Anwendung bekannter OR-Verfahren in einem Software-Projekt der Praxis.
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    Conical projection algorithms for linear programming (1989)
    Springer
    Mathematical programming 43 (1989), S. 151-173 
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    ISSN: 1436-4646
    Keywords: Conical projection methods ; Karmarkar's LP algorithm ; linear programming ; poly-nomial-time algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Linear Programming Problem is manipulated to be stated as a Non-Linear Programming Problem in which Karmarkar's logarithmic potential function is minimized in the positive cone generated by the original feasible set. The resulting problem is then solved by a master algorithm that iteratively rescales the problem and calls an internal unconstrained non-linear programming algorithm. Several different procedures for the internal algorithm are proposed, giving priority either to the reduction of the potential function or of the actual cost. We show that Karmarkar's algorithm is equivalent to this method in the special case in which the internal algorithm is reduced to a single steepest descent iteration. All variants of the new algorithm have the same complexity as Karmarkar's method, but the amount of computation is reduced by the fact that only one projection matrix must be calculated for each call of the internal algorithm.
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    On the convergence of cross decomposition (1990)
    Springer
    Mathematical programming 47 (1990), S. 269-296 
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    ISSN: 1436-4646
    Keywords: Cross decomposition ; convergence ; linear programming ; mixed integer programming ; nonlinear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Cross decomposition is a recent method for mixed integer programming problems, exploiting simultaneously both the primal and the dual structure of the problem, thus combining the advantages of Dantzig—Wolfe decomposition and Benders decomposition. Finite convergence of the algorithm equipped with some simple convergence tests has been proved. Stronger convergence tests have been proposed, but not shown to yield finite convergence. In this paper cross decomposition is generalized and applied to linear programming problems, mixed integer programming problems and nonlinear programming problems (with and without linear parts). Using the stronger convergence tests finite exact convergence is shown in the first cases. Unbounded cases are discussed and also included in the convergence tests. The behaviour of the algorithm when parts of the constraint matrix are zero is also discussed. The cross decomposition procedure is generalized (by using generalized Benders decomposition) in order to enable the solution of nonlinear programming problems.
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    Parametric linear programming and anti-cycling pivoting rules (1988)
    Springer
    Mathematical programming 41 (1988), S. 317-325 
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    ISSN: 1436-4646
    Keywords: Parametric methods ; linear programming ; anti-cycling pivoting rules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The traditional perturbation (or lexicographic) methods for resolving degeneracy in linear programming impose decision rules that eliminate ties in the simplex ratio rule and, therefore, restrict the choice of exiting basic variables. Bland's combinatorial pivoting rule also restricts the choice of exiting variables. Using ideas from parametric linear programming, we develop anticycling pivoting rules that do not limit the choice of exiting variables beyond the simplex ratio rule. That is, any variable that ties for the ratio rule can leave the basis. A similar approach gives pivoting rules for the dual simplex method that do not restrict the choice of entering variables.
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    Survey of solved and open problems in the degeneracy phenomenon (1988)
    Springer
    Mathematical programming 42 (1988), S. 125-133 
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    ISSN: 1436-4646
    Keywords: Cycling ; degeneracy ; graph theory ; linear programming ; sensitivity analysis ; simplex method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01589397
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    An algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations (1990)
    Springer
    Mathematical programming 47 (1990), S. 175-201 
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    ISSN: 1436-4646
    Keywords: Optimization ; linear programming ; complexity ; polynomial time algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present an algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations wherem is the number of constraints, andn is the number of variables. Each operation is performed to a precision of O(L) bits.L is bounded by the number of bits in the input. The worst-case running time of the algorithm is better than that of Karmarkar's algorithm by a factor of $$\sqrt {m + n} $$ .
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    Convergence behavior of interior-point algorithms (1993)
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    Mathematical programming 60 (1993), S. 215-228 
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    ISSN: 1436-4646
    Keywords: Primary 90C05 ; 90C33 ; Strict complementarity ; maximal complementarity ; interior point algorithms ; linear programming ; monotone complementarity problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that most interior-point algorithms for linear programming generate a solution sequence in which every limit point satisfies the strict complementarity condition. These algorithms include all path-following algorithms and some potential reduction algorithms. The result also holds for the monotone complementarity problem if a strict complementarity solution exists. In general, the limit point is a solution that maximizes the number of its nonzero components among all solutions.
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    Interior point algorithms for linear programming with inequality constraints (1991)
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    Mathematical programming 52 (1991), S. 209-225 
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    ISSN: 1436-4646
    Keywords: Karmarkar's algorithm ; linear programming ; projective algorithm ; conical projection ; interior methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Interior methods for linear programming were designed mainly for problems formulated with equality constraints and non-negative variables. The formulation with inequality constraints has shown to be very convenient for practical implementations, and the translation of methods designed for one formulation into the other is not trivial. This paper relates the geometric features of both representations, shows how to transport data and procedures between them and shows how cones and conical projections can be associated with inequality constraints.
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    A linear programming approach to solving bilinear programmes (1992)
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    Mathematical programming 56 (1992), S. 45-50 
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    ISSN: 1436-4646
    Keywords: Bilinear ; duality ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper discusses the maximization of a bilinear function over two independent polytopes. The maximization problem is converted into a max—min problem, using duality. This problem is then solved via a sequence of dual linear programmes, whose constraint vectors are successively determined bytth order optima of a master linear programme.
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    Gainfree Leontief substitution flow problems (1992)
    Springer
    Mathematical programming 57 (1992), S. 375-414 
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    ISSN: 1436-4646
    Keywords: Leontief matrices ; linear programming ; integer programming ; network flows ; polyhedral combinatorics ; expert systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Leontief substitution systems have been studied by economists and operations researchers for many years. We show how such linear systems are naturally viewed asLeontief substitution flow problems on directed hypergraphs, and that important solution properties follow from structural characteristics of the hypergraphs. We give a strongly polynomial, non-simplex algorithm for Leontief substitution flow problems that satisfy againfree property leading to acyclic extreme solutions. Integrality conditions follow easily from this algorithm. Another structural property,support disjoint reachability, leads to necessary and sufficient conditions for extreme solutions to be binary. In a survey of applications, we show how the Leontief flow paradigm links polyhedral combinatorics, expert systems, mixed integer model formulation, and some problems in graph optimization.
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    Symmetric indefinite systems for interior point methods (1993)
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    Mathematical programming 58 (1993), S. 1-32 
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    ISSN: 1436-4646
    Keywords: Interior point method ; linear programming ; quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is $$\left[ {\begin{array}{*{20}c} { - D^{ - 2} } & {A^T } \\ A & 0 \\ \end{array} } \right]$$ instead of reducing to obtain the usualAD 2 A T system. This methodology affords two advantages: (1) it avoids the fill created by explicitly forming the productAD 2 A T whenA has dense columns; and (2) it can easily be used to solve nonseparable quadratic programs since it requires only thatD be symmetric. We also present a procedure for converting nonseparable quadratic programs to separable ones which yields computational savings when the matrix of quadratic coefficients is dense.
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    An application of Karmarkar's interior-point linear programming algorithm for multi-reservoir operations optimization (1989)
    Springer
    Stochastic environmental research and risk assessment 3 (1989), S. 17-29 
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    ISSN: 1436-3259
    Keywords: Stochastic optimization ; linear programming ; simplex method ; Karmarkar's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated.
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    Layering strategies for creating exploitable structure in linear and integer programs (1988)
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    Mathematical programming 40 (1988), S. 165-181 
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    ISSN: 1436-4646
    Keywords: Relaxation ; network ; integer programming ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The strategy of subdividing optimization problems into layers by splitting variables into multiple copies has proved useful as a method for inducing exploitable structure in a variety of applications, particularly those involving embedded pure and generalized networks. A framework is proposed in this paper which leads to new relaxation and restriction methods for linear and integer programming based on our extension of this strategy. This framework underscores the use of constructions that lead to stronger relaxations and more flexible strategies than previous applications. Our results establish the equivalence of all layered Lagrangeans formed by parameterizing the equal value requirement of copied variables for different choices of the principal layers. It is further shown that these Lagrangeans dominate traditional Lagrangeans based on incorporating non-principal layers into the objective function. In addition a means for exploiting the layered Lagrangeans is provided by generating subgradients based on a simple averaging calculation. Finally, we show how this new layering strategy can be augmented by an integrated relaxation/restriction procedure, and indicate variations that can be employed to particular advantage in a parallel processing environment. Preliminary computational results on fifteen real world zero-one personnel assignment problems, comparing two layering approaches with five procedures previously found best for those problems, are encouraging. One of the layering strategies tested dominated all non-layering procedures in terms of both quality and solution time.
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    Preface to topics in data envelopment analysis (1984)
    Springer
    Annals of operations research 2 (1984), S. 59-94 
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    ISSN: 1572-9338
    Keywords: Efficiency ; Pareto optimality ; production functions ; returns to scale ; nondiscretionary inputs ; linear programming ; fractional programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper serves as an introduction to a series of three papers which are directed to different aspects of DEA (Data Envelopment Analysis) as follows: (1) uses and extensions of window analyses' to study DEA efficiency measures with an illustrative applications to maintenance activities for U.S. Air Force fighter wings, (2) a comparison of DEA and regression approaches to identifying and estimating, sources of inefficiency by means of artificially generated data, and (3) an extension of ordinary (linear programming) sensitivity analyses to deal with special features that require attention in DEA. Background is supplied in this introductory paper with accompanying proofs and explanations to facilitate understanding of what DEA provides in the way of underpinning for the papers that follow. An attempt is made to bring readers abreast of recent progress in DEA research and uses. A synoptic history is presented along with brief references to related work, and problems requiring attention are also indicated and possible research approaches also suggested.
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    Optimal consumption and arbitrage in incomplete, finite state security markets (1993)
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    Annals of operations research 45 (1993), S. 349-372 
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    ISSN: 1572-9338
    Keywords: Incomplete market ; trading constraints ; linear programming ; optimal portfolio ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We study a consistent treatment for both the multi-period portfolio selection problem and the option attainability problem by a dual approach. We assume that time is discrete, the horizon is finite, the sample space is finite and the number of securities is less than that of the possible securities price transitions, i.e. an incomplete security market. The investor is prohibited from investing stocks more than given linear investment amount constraints at any time and he maximizes an expected additive utility function for the consumption process. First we give a set of budget feasibility conditions so that a consumption process is attainable by an admissible portfolio process. To establish this relation, we used an algorithmic approach which has a close connection with the linear programming duality. Then we prove the unique existence of a primal optimal solution from the budget feasibility conditions. Finally, we formulate a dual control problem and establish the duality between primal and dual control problems.
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    Bounds on the number of vertices of perturbed polyhedra (1993)
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    Annals of operations research 46-47 (1993), S. 249-269 
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    ISSN: 1572-9338
    Keywords: Convex polytopes ; degeneracy ; linear programming ; simplex method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Finding the incident edges to a degenerate vertex of a polyhedron is a non-trivial problem. So pivoting methods generally involve a perturbation argument to overcome the degeneracy problem. But the perturbation entails a bursting of each degenerate vertex into a cluster of nondegenerate vertices. The aim of this paper is to give some bounds on the number of these perturbed vertices.
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    An exterior point simplex algorithm for (general) linear programming problems (1993)
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    Annals of operations research 46-47 (1993), S. 497-508 
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    ISSN: 1572-9338
    Keywords: Simplex method ; linear programming ; pivoting ; degeneracy ; exterior point algorithms ; cycling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We present an exterior point simplex type algorithm that possesses a new monotonic property. A dual feasible basic solution is required to start with. Intermediate solutions are neither primal nor dual feasible. Cycling-free pivoting rules and an exponentional example are presented.
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    Optimization using spreadsheets on a microcomputer (1985)
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    Annals of operations research 5 (1985), S. 599-612 
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    ISSN: 1572-9338
    Keywords: Microcomputers ; spreadsheets ; linear programming ; optimization ; software
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper discusses the advantages of using spreadsheets for problem specification and report generation in optimization projects. It summarizes some of the mathematical programming software which is compatible with popular spreadsheets. A small production planning problem is used to illustrate the steps in input and processing of the results. Two programs are compared in detail.
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    Parallel gradient projection successive overrelaxation for symmetric linear complementarity problems and linear programs (1988)
    Springer
    Annals of operations research 14 (1988), S. 41-59 
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    ISSN: 1572-9338
    Keywords: Parallel algorithms ; SOR ; gradient projection ; linear programming ; linear complementarity problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A gradient projection successive overrelaxation (GP-SOR) algorithm is proposed for the solution of symmetric linear complementary problems and linear programs. A key distinguishing feature of this algorithm is that when appropriately parallelized, the relaxation factor interval (0, 2) isnot reduced. In a previously proposed parallel SOR scheme, the substantially reduced relaxation interval mandated by the coupling terms of the problem often led to slow convergence. The proposed parallel algorithm solves a general linear program by finding its least 2-norm solution. Efficiency of the algorithm is in the 50 to 100 percent range as demonstrated by computational results on the CRYSTAL token-ring multicomputer and the Sequent Balance 21000 multiprocessor.
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    A dual strategy for solving the linear programming relaxation of a driver scheduling system (1995)
    Springer
    Annals of operations research 58 (1995), S. 519-531 
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    ISSN: 1572-9338
    Keywords: Driver scheduling ; multiple objectives ; linear programming ; dual simplex
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A Mathematical Programming model of a driver scheduling system is described. This consists of set covering and partitioning constraints, possibly user-supplied side constraints, and two pre-emptively ordered objectives. The previous solution strategy addressed the two objectives using separate Primal Simplex optimisations; a new strategy uses a single weighted objective function and a Dual Simplex algorithm initiated by a specially developed heuristic. Computational results are reported.
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    An effective non-Archimedean anti-degeneracy/cycling linear programming method especially for data envelopment analysis and like models (1993)
    Springer
    Annals of operations research 46-47 (1993), S. 271-278 
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    ISSN: 1572-9338
    Keywords: Degeneracy/cycling ; non-Archimedean data envelopment analysis ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A non-Archimedean effective anti-degeneracy/cycling method for linear programming models, especially Data Envelopment Analysis (DEA), processing networks and advertising media mix models is herein developed. It has given a tenfold speed increase plus elimination of cycling difficulties over conventional Marsden or Kennington/Ali LP software modules in a 1000 LP DEA application.
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    On some properties of o-degeneracy graphs (1993)
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    Annals of operations research 46-47 (1993), S. 393-408 
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    ISSN: 1572-9338
    Keywords: Degeneracy ; linear programming ; degeneracy graphs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Degenerate optima in linear programming problems lead in a canonical way to so-called o-degeneracy graphs as subgraphs of degeneracy graphs induced by the set of optimal bases. Fundamental questions about the structure of o-degeneracy graphs suggest the closer inspection of some properties of these graphs, such as, for example, the connectivity and the complexity. Finally, some open questions are pointed out.
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    An interior point method for general large-scale quadratic programming problems (1996)
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    Annals of operations research 62 (1996), S. 419-437 
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    ISSN: 1572-9338
    Keywords: Big-M Phase I procedure ; convex quadratic programming ; interior point methods ; linear programming ; method of centers ; multidirectional search direction ; nonconvex quadratic programming ; recentering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we present an interior point algorithm for solving both convex and nonconvex quadratic programs. The method, which is an extension of our interior point work on linear programming problems efficiently solves a wide class of largescale problems and forms the basis for a sequential quadratic programming (SQP) solver for general large scale nonlinear programs. The key to the algorithm is a three-dimensional cost improvement subproblem, which is solved at every interation. We have developed an approximate recentering procedure and a novel, adaptive big-M Phase I procedure that are essential to the sucess of the algorithm. We describe the basic method along with the recentering and big-M Phase I procedures. Details of the implementation and computational results are also presented.
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    Feasibility in uncapacitated networks: The effect of individual arcs and nodes (1996)
    Springer
    Annals of operations research 64 (1996), S. 197-210 
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    ISSN: 1572-9338
    Keywords: Feasibility ; uncapacitated network ; Gale-Hoffman inequality ; linear programming ; frame ; cut ; facet ; polar matrix
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The purpose of this paper is to investigate the effect of individual arcs and nodes on the description of feasibility in an uncapacitated network. This is done by developing an iterative algorithm for finding all (necessary) Gale-Hoffman inequalities for the network.
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    Bond portfolio management with repo contracts: the Italian case (2000)
    Springer
    Annals of operations research 97 (2000), S. 111-129 
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    ISSN: 1572-9338
    Keywords: repo contracts ; portfolio management ; linear programming ; 90A09 ; 90C05 ; 68U20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we present a model for management of bond portfolio including financing and investment repo contracts. Different specifications are suggested in order to reduce the problem to a linear programming problem and to consider a self-financing portfolio. The models are tested on historical data assuming a technical time scale equal to the minimum length of the contracts in the portfolio. We also compared different operative strategies on a time horizon of one month.
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    Parallel computing in combinatorial optimization (1988)
    Springer
    Annals of operations research 14 (1988), S. 245-289 
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    ISSN: 1572-9338
    Keywords: 90C27 ; 68Q15 ; 68Q25 ; 68Rxx ; Parallel computer ; computational complexity ; polylog parallel algorithm ; P-completeness ; sorting ; shortest paths ; minimum spanning tree ; matching ; maximum flow ; linear programming ; knapsack ; scheduling ; traveling salesman ; dynamic programming ; branch and bound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This is a review of the literature on parallel computers and algorithms that is relevant for combinatorial optimization. We start by describing theoretical as well as realistic machine models for parallel computations. Next, we deal with the complexity theory for parallel computations and illustrate the resulting concepts by presenting a number of polylog parallel algorithms andP-completeness results. Finally, we discuss the use of parallelism in enumerative methods.
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    On the core of the minimum cost steiner tree game in networks (1995)
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    Annals of operations research 57 (1995), S. 233-249 
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    ISSN: 1572-9338
    Keywords: Steiner tree ; game theory ; cost allocation ; integer programming ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A cost allocation problem arising from the Steiner Tree (ST) problem in networks is analyzed. This cost allocation problem is formulated as a cost cooperative game in characteristic function form, referred to as theST-game. The class ofST games generalizes the class of minimum cost spanning tree games which were used in the literature to analyze a variety of cost allocation problems. In general, the core of anST-game may be empty. We construct an efficient Core Heuristic to compute a “good” lower bound on the maximum fraction of the total cost that can be distributed among users while satisfying the core constraints. Based on the Core Heuristic, we also provide a sufficient condition for a givenST not to be optimal for the linear programming relaxation of an integer programming formulation of theST problem. The Core Heuristic was implemented and tested on 76 data sets from the literature (Wong's, Aneja's and Beasley's Steiner tree problems). Core points were found for 69 of these cases, and points “close” to the core were computed in the others.
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    A logarithmic barrier cutting plane method for convex programming (1995)
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    Annals of operations research 58 (1995), S. 67-98 
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    ISSN: 1572-9338
    Keywords: Column generation ; convex programming ; cutting plane methods ; decomposition ; interior point method ; linear programming ; logarithmic barrier function ; nonsmooth optimization ; semi-infinite programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The paper presents a logarithmic barrier cutting plane algorithm for convex (possibly non-smooth, semi-infinite) programming. Most cutting plane methods, like that of Kelley, and Cheney and Goldstein, solve a linear approximation (localization) of the problem and then generate an additional cut to remove the linear program's optimal point. Other methods, like the “central cutting” plane methods of Elzinga-Moore and Goffin-Vial, calculate a center of the linear approximation and then adjust the level of the objective, or separate the current center from the feasible set. In contrast to these existing techniques, we develop a method which does not solve the linear relaxations to optimality, but rather stays in the interior of the feasible set. The iterates follow the central path of a linear relaxation, until the current iterate either leaves the feasible set or is too close to the boundary. When this occurs, a new cut is generated and the algorithm iterates. We use the tools developed by den Hertog, Roos and Terlaky to analyze the effect of adding and deleting constraints in long-step logarithmic barrier methods for linear programming. Finally, implementation issues and computational results are presented. The test problems come from the class of numerically difficult convex geometric and semi-infinite programming problems.
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    PROMISE: A DSS for multiple objective stochastic linear programming problems (1994)
    Springer
    Annals of operations research 51 (1994), S. 45-59 
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    ISSN: 1572-9338
    Keywords: Multiple objective ; linear programming ; stochastic ; decision support system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Most of the multiple objective linear programming (MOLP) methods which have been proposed in the last fifteen years suppose deterministic contexts, but because many real problems imply uncertainty, some methods have been recently developed to deal with MOLP problems in stochastic contexts. In order to help the decision maker (DM) who is placed before such stochastic MOLP problems, we have built a Decision Support System called PROMISE. On the one hand, our DSS enables the DM to identify many current stochastic contexts: risky situations and also situations of partial uncertainty. On the other hand, according to the nature of the uncertainty, our DSS enables the DM to choose the most appropriate interactive stochastic MOLP method among the available methods, if such a method exists, and to solve his problem via the chosen method.
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    A Long-Step, Cutting Plane Algorithm for Linear and Convex Programming (2000)
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    Annals of operations research 99 (2000), S. 95-122 
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    ISSN: 1572-9338
    Keywords: cutting plane ; path following ; analytic center ; linear programming ; convex programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A cutting plane method for linear programming is described. This method is an extension of Atkinson and Vaidya's algorithm, and uses the central trajectory. The logarithmic barrier function is used explicitly, motivated partly by the successful implementation of such algorithms. This makes it possible to maintain primal and dual iterates, thus allowing termination at will, instead of having to solve to completion. This algorithm has the same complexity (O(nL 2) iterations) as Atkinson and Vaidya's algorithm, but improves upon it in that it is a “long-step” version, while theirs is a “short-step” one in some sense. For this reason, this algorithm is computationally much more promising as well. This algorithm can be of use in solving combinatorial optimization problems with large numbers of constraints, such as the Traveling Salesman Problem.
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    A combined Lagrangian, linear programming, and implication heuristic for large-scale set partitioning problems (1996)
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    Journal of heuristics 1 (1996), S. 247-259 
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    ISSN: 1572-9397
    Keywords: set partitioning ; preprocessing ; linear programming ; Lagrangian dual
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    Topics: Mathematics
    Notes: Abstract Given a finite ground set, a set of subsets, and costs on the subsets, the set partitioning problem is to find a minimum cost partition of the ground set. Many combinatorial optimization problems can be formulated as set partitioning problems. We present an approximation algorithm that produces high-quality solutions in an acceptable amount of computation time. The algorithm is iterative and combines problem size-reduction techniques, such as logical implications derived from feasibility and optimality conditions and reduced cost fixing, with a primal heuristic based on cost perturbations embedded in a Lagrangian dual framework, and cutting planes. Computational experiments illustrate the effectiveness of the approximation algorithm.
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    A Relation between Multiprocessor Scheduling and Linear Programming (1997)
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    Order 14 (1997), S. 269-278 
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    ISSN: 1572-9273
    Keywords: preemptive scheduling ; non preemptive scheduling ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The general non preemptive multiprocessor scheduling problem (NPMS) is NP-Complete, while in many specific cases, the same problem is Time-polynomial. A first connection between PMS and linear programming was established by Yannanakis, Sauer and Stone, who associated to any PMS instance some specific linear program. The main result inside this paper consists in a characterization of the partially ordered structures which allow the optimal values of any associated PMS instance to be equal to the optimal values of the corresponding linear programs.
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    Well management in the North Sea (1993)
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    Annals of operations research 43 (1993), S. 427-441 
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    ISSN: 1572-9338
    Keywords: Petroleum production ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The purpose of this paper is to describe a planning model for the management of approximately 130 petroleum-producing wells in the North Sea. The objective is to form a better basis for the decisions about which wells to produce from and which to shut down during a period. Every well is dealt with individually as the production potential and chemical composition are different. The total flow consists of six saleable components: gas, four NGL products, and oil. The production may be curtailed due to the capacities of the platforms, gathering centre, pipelines and refinery plants. The total gas production is available for fulfilling the gas contracts, injecting the gas into the reservoirs or using the gas as fuel. There exist contracts for some of the NGL products, while the rest of the NGL products and oil are sold on the free market. The well-management model is solved by means of a standard mathematical programming code, and computational results are given for a planning problem with four different data sets.
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    Multiple criteria linear programming model for portfolio selection (2000)
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    Annals of operations research 97 (2000), S. 143-162 
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    ISSN: 1572-9338
    Keywords: portfolio selection ; multiple criteria ; linear programming ; equity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The portfolio selection problem is usually considered as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model the risk is measured with variance, thus generating a quadratic programming model. The Markowitz model is frequently criticized as not consistent with axiomatic models of preferences for choice under risk. Models consistent with the preference axioms are based on the relation of stochastic dominance or on expected utility theory. The former is quite easy to implement for pairwise comparisons of given portfolios whereas it does not offer any computational tool to analyze the portfolio selection problem. The latter, when used for the portfolio selection problem, is restrictive in modeling preferences of investors. In this paper, a multiple criteria linear programming model of the portfolio selection problem is developed. The model is based on the preference axioms for choice under risk. Nevertheless, it allows one to employ the standard multiple criteria procedures to analyze the portfolio selection problem. It is shown that the classical mean-risk approaches resulting in linear programming models correspond to specific solution techniques applied to our multiple criteria model.
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    Dominant Competitive Factors for evaluating program efficiency in grouped data (1997)
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    Annals of operations research 73 (1997), S. 253-276 
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    ISSN: 1572-9338
    Keywords: Data Envelopment Analysis ; game theory ; efficiency ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Dominant Competitive Factors, unique solutions to a new class of two-person ratio efficiency games, are introduced as a means for distinguishing exceptional aspects of individual performance. The vectors of input-output multipliers thus obtained may be analyzed collectively so that commonalities within groups and differences across groups may be discovered. The method is applied to "Program Follow-Through", the original impetus for developing Data Envelopment Analysis. Our results are compared with those of the earlier study, whereupon substantial new insights are obtained.
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    A Data Envelopment Analysis approach to Discriminant Analysis (1997)
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    Annals of operations research 73 (1997), S. 299-321 
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    ISSN: 1572-9338
    Keywords: Discriminant Analysis ; linear programming ; Data Envelopment Analysis ; insurance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Data Envelopment Analysis (DEA) and Discriminant Analysis (DA) are similar in that both may be used to classify units as exhibiting either good or poor performance. Both use linear programming to select a set of factor weights that determines group membership relative to a "threshold" or hyperplane. This similarity was pointed out in an earlier paper, in which several methods which combine aspects of DA and DEA were suggested. This paper further develops one of these hybrid methods, which can be described as an efficiency approach to Discriminant Analysis. The various formulation options are considered with respect to their effects on solution quality and stability. The stability issue is raised by the fact that solution equivalence under data transformation (including both translation and rotation) is considered important in DA, and has significantly affected model formulation. Thus, the data transformation issue is studied for the hybrid method, and also for DEA. The hybrid method is applied to an insurance data set, where some firms are solvent and others in financial distress, to further evaluate the method and its possible formulations. DA methods are applied to the same data set to provide a basis for comparison. The hybrid method is shown to outperform the general discriminant models.
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    Criterion function for accessibility, uncertainty problems in regional land-use planning (1970)
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    BIT 10 (1970), S. 95-105 
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    ISSN: 1572-9125
    Keywords: Land-use planning ; accessibility ; uncertainty ; game theory ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract One objective in regional planning is the creation of communities with great accessibility. Thus we should plan the locations of inhabitants and the activities of the region so that the total accessibility will be maximized subject to some restrictions. This is a quadratic programming problem, which can be solved by quadratic programming techniques, but we cannot then take into account the uncertainties of the problem. In this paper a new criterion function is proposed for accessibility, uncertainty problems in regional land-use planning. It is derived from Hurwicz's generalized maximin principle. Many advantages are gained, for the planning problem is separated into linear programming problems, the uncertainties are taken into consideration as in game theory and the methods of parametric programming are available. A simplified problem of the populations of three town areas is studied and the method is generalized for problems of many activities and areas.
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    Ranking of vertices in the linear fractional programming problem (1983)
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    BIT 23 (1983), S. 403-405 
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    ISSN: 1572-9125
    Keywords: Vertex ranking ; fractional programming ; linear programming
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    Topics: Mathematics
    Notes: Abstract In this paper the problem of ranking vertices in the linear fractional programming problem is considered. It is shown that a class of vertex ranking algorithms for the linear programming problem can be used with only minor modifications.
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    A dual approach to detect polyhedral intersections in arbitrary dimensions (1991)
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    BIT 31 (1991), S. 2-14 
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    ISSN: 1572-9125
    Keywords: E.1 ; F.2.2 ; computational geometry ; intersection detection ; geometric duality ; multidimensional search ; hyperplane-polyhedron intersection ; polyhedron-polyhedron intersection ; arbitrary dimensions ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a dual approach to detect intersections of hyperplanes and convex polyhedra in arbitrary dimensions. Ind dimensions, the time complexities of the dual algorithms areO(2 d logn) for the hyperplane-polyhedron intersection problem, andO((2d) d−1 log d−1 n) for the polyhedron- polyhedron intersection problem. These results are the first of their kind ford 〉 3. In two dimensions, these time bounds are achieved with linear space and preprocessing. In three dimensions, the hyperplane-polyhedron intersection problem is also solved with linear space and preprocessing; quadratic space and preprocessing, however, is required for the polyhedron-polyhedron intersection problem. For generald, the dual algorithms require $$O(n^{2^d } )$$ space and preprocessing. All of these results readily extend to unbounded polyhedra.
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    Project analysis using a linear approach (P.A.U.L.A.) (1993)
    Springer
    Decisions in economics and finance 16 (1993), S. 73-86 
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    ISSN: 1129-6569
    Keywords: project analysis ; linear programming ; internal financial law (IFL) ; financial leverage ; discounted cash-flows (DCF) decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Riassunto Si definisce un modello generale (PAULA) per la valutazione, selezione e gestione ottimale di progetti certi alternativi. Sfruttando i risvolti formali e finanziari dei problemi lineari associati (diretto e duale), si formulano poi due proposte per definire una legge finanziaria interna (IFL) ottimale, utili sia per abbattere la molteplicità intrinseca delleIFL, sia per evitare risultati economicamente arbitrari nel loro uso.
    Notes: Abstract We define a general model (called PAULA) for the valuation, optimal management and selection among mutually exclusive safe projects. By exploiting the formal and financial features of the associated linear problems (primal and dual), we put forward two proposals to define an optimal internal financial law (IFL). They may be used to reduce the multiplicity of the IFLs and to avoid economically arbitrary outcomes.
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    LPL: A mathematical programming language (1993)
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    OR spectrum 15 (1993), S. 43-55 
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    ISSN: 1436-6304
    Keywords: Modeling ; linear programming ; compiler ; MPS ; Modellierung ; lineare Programmierung ; Compiler ; MPS
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Dieser Artikel beschreibt die neue Version der Modellierungssprache LPL (Linear Programming Language), die sich dazu eignet, mathematische Modelle aufzubauen, zu warten und zu dokumentieren. Die LPL-Sprache wurde zum Erstellen von MPS-InputDateien und Resultate-Tabellen größerer LP-Modelle erfolgreich eingesetzt. Der LPL-Compiler übersetzt ein LPL-Programm, das ein vollständiges Modell repräsentiert, in den Eingabecode eines LP/MIP-Lösungsprogramms, ruft den Lösungsalgorithmus auf, liest die Lösung, und ein integrierter Tabellengenerator gibt vom Benutzer definierte Resultate-Tabellen aus. Außerdem erlaubt ein Dateneingabe-Generator, die Daten in verschiedenen Formaten zu lesen.
    Notes: Summary This paper describes the new version of the modeling language, named LPL (Linear Programming Language). It may be used to build, modify and document mathematical models. The LPL language has been successfully applied to generate automatically MPS input files and reports of large LP models. The available LPL compiler translates LPL programs to the input code of any LP/MIP solver, calls the solver automatically, reads the solution back to its internal representation, and the integrated Report Generator produces the user defined reports of the model. Furthermore, an Input Generator can read the data from many formats.
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    On greedy algorithms for series parallel graphs (1988)
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    Mathematical programming 40 (1988), S. 197-204 
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    ISSN: 1436-4646
    Keywords: Greedy algorithms ; series parallel graphs ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This note describes some sufficient conditions for the maximum or minimum of a weighted flow (the weights are on paths, and are derived from weights on the edges of the path), of given volume in a series parallel graph to be found by a greedy algorithm.
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    Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems (1986)
    Springer
    Mathematical programming 35 (1986), S. 173-192 
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    ISSN: 1436-4646
    Keywords: Computational complexity ; average running time ; simplex algorithm ; linear programming ; linear complementarity problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that a particular pivoting algorithm, which we call the lexicographic Lemke algorithm, takes an expected number of steps that is bounded by a quadratic inn, when applied to a random linear complementarity problem of dimensionn. We present two probabilistic models, both requiring some nondegeneracy and sign-invariance properties. The second distribution is concerned with linear complementarity problems that arise from linear programming. In this case we give bounds that are quadratic in the smaller of the two dimensions of the linear programming problem, and independent of the larger. Similar results have been obtained by Adler and Megiddo.
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    A one-phase algorithm for semi-infinite linear programming (1990)
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    Mathematical programming 46 (1990), S. 85-103 
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    ISSN: 1436-4646
    Keywords: Semi-infinite linear programming ; generalized linear programming ; convex programming ; linear programming ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present an algorithm for solving a large class of semi-infinite linear programming problems. This algorithm has several advantages: it handles feasibility and optimality together; it has very weak restrictions on the constraints; it allows cuts that are not near the most violated cut; and it solves the primal and the dual problems simultaneously. We prove the convergence of this algorithm in two steps. First, we show that the algorithm can find anε-optimal solution after finitely many iterations. Then, we use this result to show that it can find an optimal solution in the limit. We also estimate how good anε-optimal solution is compared to an optimal solution and give an upper bound on the total number of iterations needed for finding anε-optimal solution under some assumptions. This algorithm is generalized to solve a class of nonlinear semi-infinite programming problems. Applications to convex programming are discussed.
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    Low order polynomial bounds on the expected performance of local improvement algorithms (1986)
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    Mathematical programming 35 (1986), S. 193-224 
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    ISSN: 1436-4646
    Keywords: Local improvement ; average performance of algorithms ; linear complementarity ; linear programming ; extremal set theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a general abstract model of local improvement, applicable to such diverse cases as principal pivoting methods for the linear complementarity problem and hill climbing in artificial intelligence. The model accurately predicts the behavior of the algorithms, and allows for a variety of probabilistic assumptions that permit degeneracy. Simulation indicates an approximately linear average number of iterations under a variety of probability assumptions. We derive theoretical bounds of 2en logn and en 2 for different distributions, respectively, as well as polynomial bounds for a broad class of probability distributions. We conclude with a discussion of the applications of the model to LCP and linear programming.
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    Asymptotic behaviour of Karmarkar's method for linear programming (1990)
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    Mathematical programming 46 (1990), S. 173-190 
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    ISSN: 1436-4646
    Keywords: Karmarkar's algorithm ; linear programming ; rate of convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The asymptotic behaviour of Karmarkar's method is studied and an estimate of the rate of the objective function value decrease is given. Two possible sources of numerical instability are discussed and a stabilizing procedure is proposed.
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    Relaxed variants of Karmarkar's algorithm for linear programs with unknown optimal objective value (1988)
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    Mathematical programming 40 (1988), S. 183-195 
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    ISSN: 1436-4646
    Keywords: Karmarkar's method ; linear programming ; inexact projections
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Variants of Karmarkar's algorithm are given for solving linear programs with unknown optimal objective valuez *. These new methods combine the approach of Goldfarb and Mehrotra for relaxing the requirement that certain projections be computed exactly with the approach of Todd and Burrell for generating an improving sequence of lower bounds forz * using dual feasible solutions. These methods retain the polynomial-time complexity of Karmarkar's algorithm.
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    URL: http://dx.doi.org/10.1007/BF01580729
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    A dual approach to primal degeneracy (1988)
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    Mathematical programming 42 (1988), S. 135-145 
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    ISSN: 1436-4646
    Keywords: Degeneracy ; dual infeasibility ; linear programming ; primal degeneracy ; simplex algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Revised Primal Simplex algorithm, in its simplest form, has no defence against degeneracy. Various forms of the perturbation method are usually effective, but most offer no guarantee of avoiding all degeneracy, and can lead to numerical difficulties. This paper presents a method that avoids cycling and circling by taking a dual approach. The degenerate subproblem consists of all the original variables, but only the degenerate transformed constraints. The current primal objective, which may be mixed, is used. This subproblem may be solved using the dual simplex algorithm, starting from the current dual infeasible solution, and with a zero dual objective. If the dual algorithm terminates optimally then the whole problem is optimal (subject to primal feasibility). Otherwise the final solution provides a non-basic direction which improves the value of the mixed primal objective and moves away from the degenerate vertex. A purification algorithm then renders the solution basic and further improves the mixed objective.
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    URL: http://dx.doi.org/10.1007/BF01589398
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    Interior path following primal-dual algorithms. part I: Linear programming (1989)
    Springer
    Mathematical programming 44 (1989), S. 27-41 
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    ISSN: 1436-4646
    Keywords: Interior-point methods ; linear programming ; Karmarkar's algorithm ; polynomial-time algorithms ; logarithmic barrier function ; path following
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe a primal-dual interior point algorithm for linear programming problems which requires a total of $$O\left( {\sqrt n L} \right)$$ number of iterations, whereL is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea.
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    URL: http://dx.doi.org/10.1007/BF01587075
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    Approximation algorithms for scheduling unrelated parallel machines (1990)
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    Mathematical programming 46 (1990), S. 259-271 
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    ISSN: 1436-4646
    Keywords: Scheduling ; parallel machines ; approximation algorithm ; worst case analysis ; linear programming ; integer programming ; rounding
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the following scheduling problem. There arem parallel machines andn independent jobs. Each job is to be assigned to one of the machines. The processing of jobj on machinei requires timep ij . The objective is to find a schedule that minimizes the makespan. Our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum. We also present a polynomial approximation scheme for the case that the number of machines is fixed. Both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations. In particular, we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints. In contrast to our main result, we prove that no polynomial algorithm can achieve a worst-case ratio less than 3/2 unlessP = NP. We finally obtain a complexity classification for all special cases with a fixed number of processing times.
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    URL: http://dx.doi.org/10.1007/BF01585745
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    Computational complexity of inner and outerj-radii of polytopes in finite-dimensional normed spaces (1993)
    Springer
    Mathematical programming 59 (1993), S. 163-213 
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    ISSN: 1436-4646
    Keywords: 90C30 ; 68Q15 ; 52A25 ; 90C05 ; 90C20 ; 90C25 ; 11J72 ; 11J81 ; Computational convexity ; computational complexity ; polynomial-time algorithms ; NP-hardness ; mathematical programming ; computational geometry ; ellipsoid method ; linear programming ; sensitivity analysis ; quadratic programming ; robotics ; convex body ; polarity ; polytope ; convex hull ; breadth ; width ; diameter ; radius ; insphere ; circumsphere
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper studies the complexity of computing (or approximating, or bounding) the various inner and outer radii of ann-dimensional convex polytope in the space ∝ n equipped with an ℓ p norm or a polytopal norm. The polytopeP is assumed to be presented as the convex hull of finitely many points with rational coordinates (V-presented) or as the intersection of finitely many closed halfspaces defined by linear inequalities with rational coefficients (ℋ-presented). The innerj-radius ofP is the radius of a largestj-ball contained inP; it isP's inradius whenj = n and half ofP's diameter whenj = 1. The outerj-radius measures how wellP can be approximated, in a minimax sense, by an (n — j)-flat; it isP's circumradius whenj = n and half ofP's width whenj = 1. The binary (Turing machine) model of computation is employed. The primary concern is not with finding optimal algorithms, but with establishing polynomial-time computability or NP-hardness. Special attention is paid to the case in whichP is centrally symmetric. When the dimensionn is permitted to vary, the situation is roughly as follows: (a) for general ℋ-presented polytopes in ℓ p spaces with 1〈p〈∞, all outer radius computations are NP-hard; (b) in the remaining cases (including symmetric ℋ-presented polytopes), some radius computations can be accomplished in polynomial time and others are NP-hard. These results are obtained by using a variety of tools from the geometry of convex bodies, from linear and nonlinear programming, and from the theory of computational complexity. Applications of the results to various problems in mathematical programming, computer science and other fields are included.
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    URL: http://dx.doi.org/10.1007/BF01581243
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    On the number of iterations of Karmarkar's algorithm for linear programming (1993)
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    Mathematical programming 62 (1993), S. 153-197 
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    ISSN: 1436-4646
    Keywords: Complexity analysis ; interior point methods ; Karmarkar's algorithm ; linear programming ; semi-infinite programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Karmarkar's algorithm for linear programming was published in 1984, and it is highly important to both theory and practice. On the practical side some of its variants have been found to be far more efficient than the simplex method on a wide range of very large calculations, while its polynomial time properties are fundamental to research on complexity. These properties depend on the fact that each iteration reduces a “potential function” by an amount that is bounded away from zero, the bound being independent of all the coefficients that occur. It follows that, under mild conditions on the initial vector of variables, the number of iterations that are needed to achieve a prescribed accuracy in the final value of the linear objective function is at most a multiple ofn, wheren is the number of inequality constraints. By considering a simple example that allowsn to be arbitrarily large, we deduce analytically that the magnitude of this complexity bound is correct. Specifically, we prove that the solution of the example by Karmarkar's original algorithm can require aboutn/20 iterations. Further, we find that the algorithm makes changes to the variables that are closely related to the steps of the simplex method.
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    URL: http://dx.doi.org/10.1007/BF01585165
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    A primal projective interior point method for linear programming (1991)
    Springer
    Mathematical programming 51 (1991), S. 17-43 
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    ISSN: 1436-4646
    Keywords: Interior point methods ; linear programming ; fractional linear programming ; projective algorithm ; Karmarkar's algorithm ; polynomial-type algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a new projective interior point method for linear programming with unknown optimal value. This algorithm requires only that an interior feasible point be provided. It generates a strictly decreasing sequence of objective values and within polynomial time, either determines an optimal solution, or proves that the problem is unbounded. We also analyze the asymptotic convergence rate of our method and discuss its relationship to other polynomial time projective interior point methods and the affine scaling method.
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    URL: http://dx.doi.org/10.1007/BF01586924
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    The relationship between integer and real solutions of constrained convex programming (1991)
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    Mathematical programming 51 (1991), S. 133-135 
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    ISSN: 1436-4646
    Keywords: Convex programming ; integer programming ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We prove the following theorem which gives a bound on the proximity of the real and the integer solutions to certain constrained optimization programs.
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    A survey of search directions in interior point methods for linear programming (1991)
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    Mathematical programming 52 (1991), S. 481-509 
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    ISSN: 1436-4646
    Keywords: Interior point methods ; linear programming ; potential function ; search direction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A basic characteristic of an interior point algorithm for linear programming is the search direction. Many papers on interior point algorithms only give an implicit description of the search direction. In this report we derive explicit expressions for the search directions used in many well-known algorithms. Comparing these explicit expressions gives a good insight into the similarities and differences between the various algorithms. Moreover, we give a survey of projected gradient and Newton directions for all potential and barrier functions. This is done both for the affine and projective variants.
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    A case study of resources management planning with multiple objectives and projects (1994)
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    Environmental management 18 (1994), S. 729-742 
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    ISSN: 1432-1009
    Keywords: Analytic hierarchy process ; resource allocation ; linear programming ; Olympic National Park
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Each National Park Service unit in the United States produces a resources management plan (RMP) every four years or less. The plans commit budgets and personnel to specific projects for four years, but they are prepared with little quantitative and analytical rigor and without formal decision-making tools. We have previously described a multiple objective planning process for inventory and monitoring programs (Schmoldt and others 1994). To test the applicability of that process for the more general needs of resources management planning, we conducted an exercise on the Olympic National Park (NP) in Washington State, USA. Eight projects were selected as typical of those considered in RMPs and five members of the Olympic NP staff used the analytic hierarchy process (AHP) to prioritize the eight projects with respect to their implicit management objectives. By altering management priorities for the park, three scenarios were generated. All three contained some similarities in rankings for the eight projects, as well as some differences. Mathematical allocations of money and people differed among these scenarios and differed substantially from what the actual 1990 Olympic NP RMP contains. Combining subjective priority measures with budget dollars and personnel time into an objective function creates a subjective economic metric for comparing different RMP’s. By applying this planning procedure, actual expenditures of budget and personnel in Olympic NP can agree more closely with the staff’s management objectives for the park.
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    Application of a bioeconomic strategic planning model to an industrial forest in saskatchewan (1995)
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    Water, air & soil pollution 82 (1995), S. 43-55 
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    ISSN: 1573-2932
    Keywords: optimisation ; forest modelling ; trade-offs ; industrial forestry ; linear programming ; economics ; ecosystem ; benefit distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Contemporary approaches to the issue of the allocation, conservation and management of forested land require forest managers to demonstrate the sustainability of the flow of economic, ecological and social benefits accruing from industrial use of forest resources. The integration of data sets defining these disparate resource benefits requires that they be expressed in commensurate terms such that trade-offs can be undertaken in the search for a management strategy which provides a publicly acceptable mix of benefits. To accomplish this, a new optimisation model was developed and tested for a 1.7 Mha commercial forest in west central Saskatchewan, and then used to develop 8 different forest management alternatives which were then subjected to formal evaluation procedures leading to the selection of a preferred forest management alternative.
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    URL: http://dx.doi.org/10.1007/BF01182817
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    Perch mercury content is related to acidity and color of 26 Russian lakes (1995)
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    Water, air & soil pollution 85 (1995), S. 823-828 
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    ISSN: 1573-2932
    Keywords: fish ; mercury ; lake chemistry ; biomagnification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract We determined mercury in fish (perch Perca fluviatilis) from 26 Russian lakes in three regions over four years. The lakes ranged in size from 2 to 395,000 ha, in pH from 4.5 to 10.0, and in color from 3 to 190 hazen. Sixteen lakes were drainage lakes, with permanent outlets, and 10 were seepage lakes, with no permanent inlets or outlets. The lakes were generally located in forested regions with little or no human habitation in the watershed. The three regions were geologically distinct: Precambrian Shield granitic bedrock covered with thin soil; Triassic bedrock covered with thick glacial tills; and Triassic bedrock covered with thin sediments. At each lake water samples were collected and analyzed for pH, add neutralizing capacity (ANC), major cations, and anions. Dissolved mercury species were estimated with a thermodynamic equilibrium model (MINTEQA2). Mercury content of dorsal muscle varied from 0.04 to 1.0 μg/g wet weight, and was linearly related to calculated HgCH3Cl (r20.68, p〈0.001). Lake HgCH3Cl, in turn, was related to lake pH (r2=0.86, p〈0.001). Stepwise multiple regression selected lake HgCH3Cl and color as the factors most highly related to fish mercury content, with the model accounting for 75% of the variation.
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    Development and application of a reactive plume model for mercury emissions (1995)
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    Water, air & soil pollution 80 (1995), S. 325-335 
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    ISSN: 1573-2932
    Keywords: Atmospheric chemistry ; mercury ; plume model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract A reactive plume model that includes atmospheric chemical reactions of mercury was developed. The model simulates advective transport with the mean wind flow; horizontal and vertical turbulent diffusion; gas phase; aqueous-phase and particulate chemistry; cloud microphysics; wet deposition and dry deposition. The model was applied to the simulation of clear sky, non-precipitating cloud and precipitating cloud scenarios. No significant mercury chemistry occurs in the absence of droplets. In clouds, Hg(II) is reduced to Hg(0) with more reduction taking place in precipitating clouds than in non-precipitating clouds.
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    URL: http://dx.doi.org/10.1007/BF01189682
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    Denuder-based techniques for sampling, separation and analysis of gaseous and participate mercury in air (1995)
    Springer
    Water, air & soil pollution 80 (1995), S. 1209-1216 
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    ISSN: 1573-2932
    Keywords: gaseous ; particulate ; mercury ; sampling ; silver ; gold ; denuder
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract A denuder-based method for sampling and separating gaseous and participate mercury in the air is described. Two different denuder configurations developed in Vilnius, Lithuania (silver) and in Gothenburg, Sweden (gold) are compared. Data were acquired at different sampling locations around the cities of Vilnius and Gothenburg. The concentration of particulate Hg was found to be 0.04 to 0.40 ng m−3 in the Vilnius region, and 0.11 to 0.57 ng m−3 in the Gothenburg region. Intel-calibration results for the silver and gold denuders are presented. The results obtained by the two different denuder configurations and sampling set-ups display satisfactory agreement.
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    Mercury concentrations in forest trees from Slovakia (1996)
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    Water, air & soil pollution 89 (1996), S. 267-275 
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    ISSN: 1573-2932
    Keywords: mercury ; forest trees ; biomonitors ; contaminants
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract The concentration of mercury has been determined in assimilation organs of forest trees from 10 main industrial regions of Slovakia, four mountain forests and one military area and compared with concentration of mercury from 1356 permanent monitoring plots of Slovakia. The mercury concentration ranges for 2 yr old needles of Picea abies Karst. were (in mg kg−1): 1.249–4.402 (Rudnany iron ore mines), 0.013–0.749 (nine other industrial regions), 0.021–0.737 (four mountain forests) and 0.053–0.538 (military area). The mercury content in the soil (0–5 cm) from a mercury smelting plant ranged from 9.9 to 130 mg kg−1, and the moss Pleurozium schreberi contained 3.8–9.1 mg kg−1. The values obtained were compared with the available literature data.
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    MODELLING LEACHING OF INORGANIC Hg(II) IN A SCANDINAVIAN IRON-HUMUS PODZOL - VALIDATION AND LONG-TERM LEACHING UNDER VARIOUS DEPOSITION RATES (1997)
    Springer
    Water, air & soil pollution 96 (1997), S. 301-320 
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    ISSN: 1573-2932
    Keywords: acid rain ; batch experiment ; Freundlich isotherm ; lysimeter experiment ; mercury ; simulation model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Increasing mercury contents are reported from freshwater systems and fish in northern Europe and North America. Mercury input from soils is a major source with the leaching being affected by increased atmospheric mercury deposition compared to pre-industrial times and by other environmental conditions such as acid rain. The results of a mathematical model-calculation of vertical inorganic Hg(II) leaching in a Scandinavian iron-humus podzol under different atmospheric input rates of mercury are presented. Leaching under background rain conditions was calculated to be considerably stronger than under acid rain conditions. Increasing fractions of deposited soluble or solute atmospheric mercury were leached from the O f(h)-horizon with decreasing soil content of soluble mercury under acid rain conditions; this effect was less pronounced under background rain conditions. The steady state concentrations of soluble mercury of the upper soil horizons were calculated and compared with the actual concentrations of total (= soluble + insoluble mercury) and extractable (= estimate of soluble) mercury measured in these horizons. The results indicate that even if the deposition of airborne mercury to soil is strongly reduced, the total mercury content of the soil decreases only slowly. It may take decades or even centuries before a new steady state concentration of total mercury is established in the soil. The decrease of the mercury concentration in the O f(h)-horizon is probably largely dependent on the turnover of organic matter, binding most of the deposited airborne mercury in an insoluble form. Hence, present day mercury leaching is likely to be dominated by mercury deposited during former times and temporarily retained in an insoluble form in the organic matter.
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    URL: http://dx.doi.org/10.1023/A:1026476921969
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    The role of humic substances in the aqueous mobilization of mercury from contaminated floodplain soils (1996)
    Springer
    Water, air & soil pollution 90 (1996), S. 507-520 
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    ISSN: 1573-2932
    Keywords: mercury ; foodplains ; humic substances ; complexation ; speciation ; mobilization ; risk assessment ; water solubility
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract The water-mobilizability of mercury from contaminated floodplain soils of the river Elbe in Northern Germany was evaluated by batch extraction experiments. It was shown that only a small amount of the total mercury present (about 1% per extraction) can be mobilized by water. This mercury is transported entirely in the form of a complex bound to humic acids (HA); particulates and fulvic acids (FA) did not seem to contribute to the process. It could not be removed from the HA even at pH 1, indicating an extremely strong complexation e.g. by sulfur-containing ligands. Furthermore, the influence of pH on the mobilization was investigated. It was found that in the range of natural pH-values, there was no observable effect of pH on the mobilization of either mercury or dissolved organic carbon (DOC). This surprising finding is explained by an unexpectedly high buffering capacity of the humics, both in the acidic and in the alkaline region. Only at extreme pH-values there was deviation from this behaviour. In contrast to other heavy metals, the amount of mobilized mercury decreases at pH 〈 3; and at pH 〉 12, an increased mobilization of mercury was observed because the humics are mobilized completely, accompanied by the total amount of mercury bound to them.
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    Global mercury pollution and the role of gold mining: An overview (1997)
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    Water, air & soil pollution 97 (1997), S. 205-207 
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    ISSN: 1573-2932
    Keywords: mercury ; gold mining ; ecosystems ; methyl-Hg ; cycling ; global sources
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract As described by Jemelov and Ramel (1995), the Scientific Committee on Problems of the Environment (SCOPE) sponsored an investigation of Hg in ecosystems with special emphasis on tropical regions. In these regions small-scale gold mining activities have occupied about 10 million people worldwide who use Hg for extracting gold.
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    Determination of atmospheric mercury during the North sea experiment (1997)
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    Water, air & soil pollution 97 (1997), S. 257-263 
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    ISSN: 1573-2932
    Keywords: mercury ; atmosphere ; rainwater ; marine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Total gaseous mercury (TGM) and rainwater were collected on board of two research vessels (F. S. ALKOR and R.V. BELGICA) positioned 200 km apart in the center of the North Sea during the North Sea Experiment, September 1991. On the F. S. ALKOR (up-wind ship) TGM concentrations ranged from 0.7 to 2.6 ng·m−3 with an average of 1.5 ng m−3 and on the R. V. BELGICA (down-wind ship) TGM ranged from 0.7 to 1.9 ng·m−3 with an average of 1.2 ng·m−3. An average 20% decrease is observed from the up-wind to the down wind ship. which may largely be affected by entrainment into the free troposphere. An overall removal (entrainment) velocity of 0.95 cm·s−1 was calculated for the whole experiment. The average removal velocity was 0.5 cm·s−1 for dry periods and varied between 1 to 5 cm·s−1 during rain events. Rainwater concentrations varied between 5 and 25 ng·1−1. Based on these data an annual wet deposition flux of 1.08 ng Hg cm−2 yr1− was estimated for the North Sea.
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    TOTAL MERCURY AND METHYLMERCURY IN SEDIMENTS AND IN THE POLYCHAETE NEREIS DIVERSICOLOR AT GROOT BUITENSCHOOR (SCHELDT ESTUARY, BELGIUM) (1997)
    Springer
    Water, air & soil pollution 94 (1997), S. 109-123 
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    ISSN: 1573-2932
    Keywords: mercury ; methylmercury ; sediment ; polychaete ; Nereis diversicolor ; methylation ; bioaccumulation ; Scheldt estuary
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Total mercury (Hg) and methylmercury (MeHg) concentrations were determined in sediments and in the polychaete worm Nereis diversicolor at 13 stations of a brackish water intertidal mudflat of the Scheldt estuary. Hg and MeHg concentrations in sediments ranged from 144 to 1192 ng g−1 dw and from 0.8 to 6 ng g−1 dw, respectively. Both Hg and MeHg concentrations increased with an increase of organic matter (OM) content and fine grain fraction. In contrast, Hg accumulation by N. diversicolor was significantly (p 〈 0.05) higher at stations with sandy sediments (mean value: 125 ng g−1 dw) than at stations with muddy sediments (mean value, 80 ng g−1), probably because Hg availability for bioaccumulation at muddy stations was reduced by high OM content of the muddy sediments. MeHg accounted for an average of 0.7% of the total Hg in sediments and 18% of the total Hg in N. diversicolor. Seasonal variations significantly affected Hg concentrations in sediments and MeHg in N. diversicolor. Total Hg concentrations in sediments were significantly (p 〈 0.05) higher in autumn and winter than in spring and summer whereas MeHg concentrations were lowest in winter compared to the other seasons. On the other hand, total Hg concentrations in the worms were lowest in spring whereas MeHg concentrations were significantly (p 〈 0.01) higher in spring and summer than in autumn and winter.
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    URL: http://dx.doi.org/10.1023/A:1026434629599
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    Comparison of two reagents, sodium pyrophosphate and sodium hydroxide, in the extraction of labile metal organic complexes (1997)
    Springer
    Water, air & soil pollution 99 (1997), S. 217-223 
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    ISSN: 1573-2932
    Keywords: selective leach ; organic ; humic ; fulvic ; analysis ; mercury ; zinc
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract The international reference lake sediment, LKSD-4, was used to compare Hg, organic C and Zn extracted from its ‘soluble organic’ phase by two commonly used reagents: 0.1 M Na4P2O7 solution at pH 10 and 0.5 M NaOH solution at pH 12. While recoveries of Hg and Zn by 0.1 M Na4P2O7 are not affected by changes in sample weight to reagent volume ratio (W/V) or contact time, those by NaOH show a marked dependency. In general, the NaOH leach extracts more organic C and Hg from LKSD-4 but less Zn. Over the range of conditions studied, the NaOH-based method extracted 4.7–9.8% C, 27–103 ng g−1 Hg and 19–69 μg g−1 Zn from LKSD-4, compared to 2.3–2.8% C, 17–24 ng g−1 Hg and 64–72 μg g−1 Zn by the Na4P2O7 leach. Clearly, different groups of organic substances are being dissolved by these two reagents and therefore a comparison of data from different laboratories becomes meaningless. This paper suggests that more research is needed into the exactNature of metal-organic associations extracted by selective leaches and into associated artifacts of extraction such as readsorption phenomena.
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    URL: http://dx.doi.org/10.1007/BF02406861
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    Mercury dynamics in young Common Tern (Sterna hirundo) chicks from a polluted environment (1993)
    Springer
    Ecotoxicology 2 (1993), S. 33-40 
    Details
    ISSN: 1573-3017
    Keywords: mercury ; body distribution ; feather concentrations ; body burden ; tern chicks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: We studied mercury concentrations and amounts in tissues of 19 starved young Common Tern chicks (median age 4 days) and in eggs from the same colony. Concentrations and burden were similar between eggs and newly hatched chicks. Mercury concentrations were highest in down, which contained at least 38% of the body mercury. The mercury burden of the whole body and of the tissues as well as the concentration in down increased with age and body mass, indicating the importance of down as an elimination pathway. Conversion ratios between mercury concentrations in tissues and the whole chick body varied according to the contamination level.
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    URL: http://dx.doi.org/10.1007/BF00058212
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    Allozymes Reflect the Population-Level Effect of Mercury: Simulations of the Mosquitofish (Gambusia holbrooki Girard) GPI-2 Response (1998)
    Springer
    Ecotoxicology 7 (1998), S. 141-150 
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    ISSN: 1573-3017
    Keywords: fish ; mercury ; natural selection ; allozyme ; population
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Measurements of the differential tolerance between enzyme genotypes and shifts in allozyme frequencies in populations from contaminated habitats have prompted the use of allozymes as markers of population-level toxicant effects. However, such studies often do not consider other factors that influence allele frequencies, including natural clines, migration, the intensity and specificity of selection and toxicant-induced genetic bottlenecks. In addition, selection components other than survival are not included. Consequently, the associated conclusions remain speculative. To assess this approach rigorously, a simulation study was conducted with the mosquitofish (Gambusia holbrooki) GPI-2 locus. Laboratory studies have shown the GPI-238/38 homozygote at this locus to be less tolerant than other genotypes during acute exposure to mercury. The GPI-2100/100 genotype has also been shown to have a reproductive disadvantage at lower mercury concentrations. Simple and then more complex models were used to quantify the relative effects of viability selection, random genetic drift and migration on the GPI-238 allele frequency. Simulations were also performed to assess the contribution of sexual and fecundity selection. A simple population model suggested that viability selection plays a greater role than does mortality-driven, genetic drift in the decrease of the sensitive allele under the conditions of this study. A more complex, stochastic model indicated that no significant mortality-driven drift was taking place in this system. In both models, migration mitigated the effect of selection. Sexual and fecundity selection had little effect on the allele frequencies in these simulations. We conclude that, provided the system under study is clearly understood, shifts in allele frequency can indicate the population-level effects of pollutants.
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    URL: http://dx.doi.org/10.1023/A:1014352226686
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    A linear programming approach to reasoning about probabilities (1990)
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    Annals of mathematics and artificial intelligence 1 (1990), S. 189-205 
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    ISSN: 1573-7470
    Keywords: Probabilistic logic ; reasoning about probabilities ; linear programming ; algorithms ; complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We continue our study, initiated in [9], of the following computational problem proposed by Nilsson: Several clauses (Boolean functions of several variables) are given, and for each clause the probability that the clause is true is specified. We are asked whether these probabilities are consistent. They are if there is a probability distribution on the truth assignments such that the probability of each clause is the measure of its satisfying set of assignments. Since this is a generalization of the satisfiability problem of predicate calculus, it is immediately NP-hard. In [9] we showed certain restricted cases of the problem to be NP-complete, and used the Ellipsoid Algorithm to show that a certain special case is in P. In this paper we use the Simplex method, column generation techniques, and variable-depth local search to derive an effective heuristic for the general problem. Experiments show that our heuristic performs successfully on instances with many dozens of variables and clauses. We also prove several interesting complexity results that answer open questions in [9] and motivate our approach.
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    URL: http://dx.doi.org/10.1007/BF01531078
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    Mathematical analysis of some neural networks for solving linear and quadratic programming (1996)
    Springer
    Acta mathematicae applicatae sinica 12 (1996), S. 1-10 
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    ISSN: 1618-3932
    Keywords: Neural network ; linear programming ; quadratic programming ; penalty function method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Artificial neural network techniques have been introduced into the area of optimization in the recent decade. Some neural network models have been suggested to solve linear and quadratic programming problems. The Kennedy and Chua model[5] is one of these networks. In this paper results about the convergence of the model are obtained. Another related problem is how to choose a parameter value $$\tilde s$$ so that the equilibrium point of the network immediately and properly approximates the original solution. Such an estimation for the parameter is given in a closed form when the network is used to solve linear programming.
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    URL: http://dx.doi.org/10.1007/BF02009555
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    Adaptive use of iterative methods in predictor–corrector interior point methods for linear programming (2000)
    Springer
    Numerical algorithms 25 (2000), S. 387-406 
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    ISSN: 1572-9265
    Keywords: interior point methods ; linear programming ; iterative methods for linear systems ; adaptive algorithms ; self-timing algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this work we devise efficient algorithms for finding the search directions for interior point methods applied to linear programming problems. There are two innovations. The first is the use of updating of preconditioners computed for previous barrier parameters. The second is an adaptive automated procedure for determining whether to use a direct or iterative solver, whether to reinitialize or update the preconditioner, and how many updates to apply. These decisions are based on predictions of the cost of using the different solvers to determine the next search direction, given costs in determining earlier directions. We summarize earlier results using a modified version of the OB1-R code of Lustig, Marsten, and Shanno, and we present results from a predictor–corrector code PCx modified to use adaptive iteration. If a direct method is appropriate for the problem, then our procedure chooses it, but when an iterative procedure is helpful, substantial gains in efficiency can be obtained.
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    URL: http://dx.doi.org/10.1023/A:1016614603137
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    Numerical solution of positive control problem via linear programming (1994)
    Springer
    Numerical algorithms 8 (1994), S. 185-199 
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    ISSN: 1572-9265
    Keywords: Basis ; feasible solution ; controllability ; linear programming ; reachability ; simplex method ; time optimal control ; 65 K
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The reachability problem for linear time-invariant discrete-time control systems with sign-restricted input is considered. The time-optimal control is constructed by an iterative procedure. Each step of the iteration is defined as a linear programming problem. This problem is solved by the simplex algorithm. The initial feasible solution for the simplex algorithm is provided by the preceding step of the iteration. The inversion of the basis matrix is reduced to a bordering procedure. The structural stability of the solution is investigated.
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    URL: http://dx.doi.org/10.1007/BF02142690
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    Solving high-index DAEs by Taylor series (1998)
    Springer
    Numerical algorithms 19 (1998), S. 195-211 
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    ISSN: 1572-9265
    Keywords: algorithms ; combinatorics ; linear programming ; Taylor series ; index ; assignment problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a general method of solving differential-algebraic equations by expanding the solution as a Taylor series. It seems especially suitable for (piecewise) smooth problems of high index. We describe the method in general, discuss steps to be taken if the method, as initially applied, fails because it leads to a system of equations with identically singular Jacobian, and illustrate by solving two problems of index 5.
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    URL: http://dx.doi.org/10.1023/A:1019150322187
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    Moment problem formulation of the Schrödinger equation (1992)
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    Numerical algorithms 3 (1992), S. 1-16 
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    ISSN: 1572-9265
    Keywords: Moment problem ; Schrödinger equation ; inequalities ; convexity ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that it is possible to project out in an exact manner the lowest eigenstate of Schrödinger equations. Taking into account the nodeless property of the lowest eigenstate one can replace the full Schrödinger equation by a moment problem whose measure is the eigenstate itself. The infinite set of positivity inequalities linked to this moment problem provides a framework which allows to compute sequences of upper and lower bounds to the unknown eigenvalue and eigenfunction. The effective computation is based on deep convexity properties embedded in the set of hierarchical inequalities associated to this moment problem. The convexity allows to get the bounds through linear programming. We illustrate the method with simple one dimensional problems.
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    URL: http://dx.doi.org/10.1007/BF02141911
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    Extinction-angle distribution of plagioclase feldspars in clastic sediments (1975)
    Springer
    Mathematical geology 7 (1975), S. 335-348 
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    ISSN: 1573-8868
    Keywords: optical mineralogy ; clastic plagioclase ; linear programming ; provenance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An extinction-angle distribution was computed for randomly oriented grains of plagioclase feldspar with a known An-composition. Expressed by a histogram with eighteen columns, the results are shown by an 18×19 data array for nineteen types of low-temperature plagioclase. In a mixture of grains with various An-compositions, the extinction-angle distribution is given by a linear combination of the obtained data matrix with the frequencies of An-composition. If we have a sample containing randomly oriented grains of plagioclase feldspars, a frequency distribution of those with An-composition can be calculated after measuring their extinction angles. By taking into account the constraints of inequalities, the calculation is treated with the dual method of linear programming. The procedure provides for a simpler and more expedient method for determining the frequency distribution of An-composition. This method was tested by applying it to a model sample containing randomly oriented plagioclase grains with known An-composition frequencies, whose extinction-angle distribution was determined by the Monte Carlo method. An example of application of this method to Permian sandstones from central Japan is presented.
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    URL: http://dx.doi.org/10.1007/BF02081705
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    The impact of assumptions about oil exploration on projections of long-range energy supplies in the United States (1977)
    Springer
    Mathematical geology 9 (1977), S. 429-439 
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    ISSN: 1573-8868
    Keywords: long-range energy modeling ; linear programming ; exploratory drilling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A large-scale linear programming model has been designed to assist in the analysis of world-wide energy resource development and processing activities over a 20- to 30-year time horizon. the model includes explicit representation of exploration and production operations for the energy minerals, as well as the supply, conversion, and distribution of the different energy forms, accounting for interfuel substitution alternatives. The method of analysis consists of developing “optimal” planning solutions relative to anticipated demands for energy and using these solutions as bases for evaluation of energy policies and technology assumptions. This paper briefly outlines the representation of the exploration activities in the overall model formulation and illustrates the projected energy supply patterns and related economics as developed with the model for alternative assumptions about oil resources, exploration success rates, and constraints on exploratory drilling.
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    URL: http://dx.doi.org/10.1007/BF02047412
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    An oblique factor analysis solution for the analysis of mixtures (1978)
    Springer
    Mathematical geology 10 (1978), S. 225-241 
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    ISSN: 1573-8868
    Keywords: factor analysis ; linear programming ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The problems involved in the factor analysis of data consisting of measurements of material quantity or proportion are discussed, and the inability of existing factor analysis solutions to properly model such data is pointed out. A new factor analysis solution using the linear programming technique is presented which properly analyzes mixture data. A numerical example is presented in which a body of suspended sediment grain-size distribution data is analyzed using the new factor analysis solution. FORTRAN-IV subroutines for computing this solution are included in an Appendix.
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    URL: http://dx.doi.org/10.1007/BF01032865
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    Resource estimation from historical data: Mercury, a test case (1980)
    Springer
    Mathematical geology 12 (1980), S. 489-522 
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    ISSN: 1573-8868
    Keywords: mercury ; resource estimation ; production data
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A simple technique based on historical records of tonnage and grade of ore produced provides a means for calculating how much of a mineral product will be available in the future at various average grades. Estimates made on this basis are independent of geologic considerations or changing economic and political factors, although they are based on mining history, which was largely determined by these factors. The relatively minor element, mercury, was used for the test case reported here, but the method has been found applicable to forecasts of resources for other mineral products. Mercury resources available in ore in which the average grade is as low as 0.1% are estimated to be 53 ×10 6 kg (1.5 ×10 6 flasks) for the United States and 1551 ×10 6 kg (45 ×10 6 flasks) for the world; this amount is more than adequate to meet predicted demand to the year 2000. The expectable price of mercury in 1978 dollars at this 0.1% grade is projected to be $58.75 per kg ($2,025 per flask), but at a 10% annual inflation rate, it would be more than $12,000 per flask. To satisfy just the projected U.S. demand for mercury by 2000, the price is calculated to be $48.96 per kg ($1,688 per flask) in 1978 dollars at an average annual grade of 0.12%.
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    URL: http://dx.doi.org/10.1007/BF01028882
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    Designs in Product Association Schemes (1999)
    Springer
    Designs, codes and cryptography 16 (1999), S. 271-289 
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    ISSN: 1573-7586
    Keywords: Association scheme ; block design ; orthogonal array ; partially ordered set ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A number of important families of association schemes—such as the Hamming and Johnson schemes—enjoy the property that, in each member of the family, Delsarte t-designs can be characterised combinatorially as designs in a certain partially ordered set attached to the scheme. In this paper, we extend this characterisation to designs in a product association scheme each of whose components admits a characterisation of the above type. As a consequence of our main result, we immediately obtain linear programming bounds for a wide variety of combinatorial objects as well as bounds on the size and degree of such designs analogous to Delsarte's bounds for t-designs in Q-polynomial association schemes.
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    URL: http://dx.doi.org/10.1023/A:1008340128973
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    Local decomposition of gray-scale morphological templates (1992)
    Springer
    Journal of mathematical imaging and vision 2 (1992), S. 39-50 
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    ISSN: 1573-7683
    Keywords: image processing ; linear programming ; mathematical morphology ; image algebra ; template decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Template decomposition techniques can be useful for improving the efficiency of imageprocessing algorithms. The improved efficiency can be realized either by reorganizing a computation to fit a specialized structure, such as an image-processing pipeline, or by reducing the number of operations used. In this paper two techniques are described for decomposing templates into sequences of 3×3 templates with respect to gray-scale morphological operations. Both techniques use linear programming and are guaranteed to find a decomposition of one exists.
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    URL: http://dx.doi.org/10.1007/BF00123880
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