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  • Articles  (102)
  • Linear programming  (74)
  • kinetics
  • nitrogen
  • Springer  (102)
  • Periodicals Archive Online (PAO)
  • 1990-1994  (102)
  • Mathematics  (75)
  • Geosciences  (28)
  • 1
    Electronic Resource
    Electronic Resource
    Polynomiality of infeasible-interior-point algorithms for linear programming (1994)
    Springer
    Mathematical programming 67 (1994), S. 109-119 
    Details
    ISSN: 1436-4646
    Keywords: Polynomial-time ; Linear programming ; Primal-dual ; Interior-point algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Kojima, Megiddo, and Mizuno investigate an infeasible-interior-point algorithm for solving a primal—dual pair of linear programming problems and they demonstrate its global convergence. Their algorithm finds approximate optimal solutions of the pair if both problems have interior points, and they detect infeasibility when the sequence of iterates diverges. Zhang proves polynomial-time convergence of an infeasible-interior-point algorithm under the assumption that both primal and dual problems have feasible points. In this paper, we show that a modification of the Kojima—Megiddo—Mizuno algorithm “solves” the pair of problems in polynomial time without assuming the existence of the LP solution. Furthermore, we develop anO(nL)-iteration complexity result for a variant of the algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582216
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  • 2
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    Random walks, totally unimodular matrices, and a randomised dual simplex algorithm (1994)
    Springer
    Mathematical programming 64 (1994), S. 1-16 
    Details
    ISSN: 1436-4646
    Keywords: Random walks ; Totally unimodular matrices ; Uniform generation ; Linear programming ; Diameter of polytopes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We discuss the application of random walks to generating a random basis of a totally unimodular matrix and to solving a linear program with such a constraint matrix. We also derive polynomial upper bounds on the combinatorial diameter of an associated polyhedron.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582563
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  • 3
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    Dynamic factorization in large-scale optimization (1994)
    Springer
    Mathematical programming 64 (1994), S. 17-51 
    Details
    ISSN: 1436-4646
    Keywords: Factorization ; Linear programming ; Generalized upper bounds ; Pure networks ; Generalized networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Factorization of linear programming (LP) models enables a large portion of the LP tableau to be represented implicitly and generated from the remaining explicit part. Dynamic factorization admits algebraic elements which change in dimension during the course of solution. A unifying mathematical framework for dynamic row factorization is presented with three algorithms which derive from different LP model row structures: generalized upper bound rows, pure network rows, and generalized network rows. Each of these structures is a generalization of its predecessors, and each corresponding algorithm exhibits just enough additional richness to accommodate the structure at hand within the unified framework. Implementation and computational results are presented for a variety of real-world models. These results suggest that each of these algorithms is superior to the traditional, non-factorized approach, with the degree of improvement depending upon the size and quality of the row factorization identified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582564
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  • 4
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    Interior-point algorithms for semi-infinite programming (1994)
    Springer
    Mathematical programming 65 (1994), S. 217-245 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; Semi-infinite programming ; Interior-point methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In order to study the behavior of interior-point methods on very large-scale linear programming problems, we consider the application of such methods to continuous semi-infinite linear programming problems in both primal and dual form. By considering different discretizations of such problems we are led to a certain invariance property for (finite-dimensional) interior-point methods. We find that while many methods are invariant, several, including all those with the currently best complexity bound, are not. We then devise natural extensions of invariant methods to the semi-infinite case. Our motivation comes from our belief that for a method to work well on large-scale linear programming problems, it should be effective on fine discretizations of a semi-infinite problem and it should have a natural extension to the limiting semi-infinite case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581697
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  • 5
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    The maximum entropy method on the mean: Applications to linear programming and superresolution (1994)
    Springer
    Mathematical programming 66 (1994), S. 103-122 
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    ISSN: 1436-4646
    Keywords: 42B05 ; 62A99 ; Maximum entropy ; Linear programming ; Inverse problems ; Superresolution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we give two different results. We propose new methods to solve classical optimization problems in linear programming. We also obtain precise quantitative results for the superresolution phenomenon, as observed earlier by practical searchers on specific algorithms. The common background of our work is the generalized moment problem, which is known to be connected with linear programming and superresolution. We describe the Maximum Entropy Method on the Mean that provides solution to the problem and leads to computational criteria to decide the existence of solutions or not.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581139
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  • 6
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    Superlinear convergence of infeasible-interior-point methods for linear programming (1994)
    Springer
    Mathematical programming 66 (1994), S. 361-377 
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    ISSN: 1436-4646
    Keywords: Linear programming ; Infeasible-interior-point methods ; Superlinear convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract At present the interior-point methods of choice are primal—dual infeasible-interior-point methods, where the iterates are kept positive, but allowed to be infeasible. In practice, these methods have demonstrated superior computational performance. From a theoretical point of view, however, they have not been as thoroughly studied as their counterparts — feasible-interior-point methods, where the iterates are required to be strictly feasible. Recently, Kojima et al., Zhang, Mizuno and Potra studied the global convergence of algorithms in the primal—dual infeasible-interior-point framework. In this paper, we continue to study this framework, and in particular we study the local convergence properties of algorithms in this framework. We construct parameter selections that lead toQ-superlinear convergence for a merit function andR-superlinear convergence for the iteration sequence, both at rate 1 +τ whereτ can be arbitrarily close to one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581155
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  • 7
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    Limiting behavior of weighted central paths in linear programming (1994)
    Springer
    Mathematical programming 65 (1994), S. 347-363 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; (Weighted) central paths ; Limiting behavior on central paths ; Local convergence rates of interior point algorithms ; Primary: 90C05 ; Secondary: 90C33
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We study the limiting behavior of the weighted central paths{(x(μ), s(μ))} μ 〉 0 in linear programming at bothμ = 0 andμ = ∞. We establish the existence of a partition (B ∞,N ∞) of the index set { 1, ⋯,n } such thatx i(μ) → ∞ ands j (μ) → ∞ asμ → ∞ fori ∈ B ∞, andj ∈ N ∞, andx N∞ (μ),s B∞ (μ) converge to weighted analytic centers of certain polytopes. For allk ⩾ 1, we show that thekth order derivativesx (k) (μ) ands (k) (μ) converge whenμ → 0 andμ → ∞. Consequently, the derivatives of each order are bounded in the interval (0, ∞). We calculate the limiting derivatives explicitly, and establish the surprising result that all higher order derivatives (k ⩾ 2) converge to zero whenμ → ∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581702
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  • 8
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    Asymptotic analysis of the exponential penalty trajectory in linear programming (1994)
    Springer
    Mathematical programming 67 (1994), S. 169-187 
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    ISSN: 1436-4646
    Keywords: 90C05 ; 90C25 ; 90C31 ; 49M30 ; Linear programming ; Exponential penalty ; Optimal trajectory ; Asymptotic expansion ; Interior point methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the linear program min{c′x: Ax⩽b} and the associated exponential penalty functionf r(x) = c′x + rΣexp[(A ix − bi)/r]. Forr close to 0, the unconstrained minimizerx(r) off r admits an asymptotic expansion of the formx(r) = x * + rd* + η(r) wherex * is a particular optimal solution of the linear program and the error termη(r) has an exponentially fast decay. Using duality theory we exhibit an associated dual trajectoryλ(r) which converges exponentially fast to a particular dual optimal solution. These results are completed by an asymptotic analysis whenr tends to ∞: the primal trajectory has an asymptotic ray and the dual trajectory converges to an interior dual feasible solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582220
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  • 9
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    A quadratically convergent predictor—corrector method for solving linear programs from infeasible starting points (1994)
    Springer
    Mathematical programming 67 (1994), S. 383-406 
    Details
    ISSN: 1436-4646
    Keywords: 90C05 ; Linear programming ; Primal—dual ; Polynomial complexity ; Infeasible ; Interior-point ; Exterior-point
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A predictor—corrector method for solving linear programs from infeasible starting points is analyzed. The method is quadratically convergent and can be combined with Ye's finite termination scheme under very general assumptions. If the starting points are large enough then the algorithm hasO(nL) iteration complexity. If the ratio between feasibility and optimality at the starting points is small enough then the algorithm has O( $$\sqrt {n L} $$ ) iteration complexity. For feasible starting points the algorithm reduces to the Mizuno—Todd—Ye predictor—corrector method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582228
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  • 10
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    Constant potential primal—dual algorithms: A framework (1994)
    Springer
    Mathematical programming 66 (1994), S. 145-159 
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    ISSN: 1436-4646
    Keywords: Linear programming ; Interior point methods ; Primal—dual algorithms ; Potential function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We start with a study of the primal—dual affine-scaling algorithms for linear programs. Using ideas from Kojima et al., Mizuno and Nagasawa, and new potential functions we establish a framework for primal—dual algorithms that keep a potential function value fixed. We show that if the potential function used in the algorithm is compatible with a corresponding neighborhood of the central path then the convergence proofs simplify greatly. Our algorithms have the property that all the iterates can be kept in a neighborhood of the central path without using any centering in the search directions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581142
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  • 11
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    Historical changes in sediments of Pyramid Lake, Nevada, USA: consequences of changes in the water balance of a terminal desert lake (1994)
    Springer
    Journal of paleolimnology 12 (1994), S. 87-101 
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    ISSN: 1573-0417
    Keywords: Great Basin ; climatic variations ; productivity ; organic matter ; nitrogen ; phosphorus ; hardwater lake
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences
    Notes: Abstract Sediment cores from the shallow and deep basins of Pyramid Lake, Nevada, revealed variations in composition with depth reflecting changes in lake level, river inflow, and lake productivity. Recent sediments from the period of historical record indicate: (1) CaCO3 and organic content of sediment in the shallow basin decrease at lower lake level, (2) CaCO3 content of deep basin sediments increases when lake level decreases rapidly, and (3) the inorganic P content of sediments increases with decreasing lake volume. Variations in sediment composition also indicate several periods for which productivity in Pyramid Lake may have been elevated over the past 1000 years. Our data provide strong evidence for increased productivity during the first half of the 20th Century, although the typical pattern for cultural eutrophication was not observed. The organic content of sediments also suggests periods of increased productivity in the lake prior to the discovery and development of the region by white settlers. Indeed, a broad peak in organic fractions during the 1800's originates as an increase starting around 1600. However, periods of changing organic content of sediments also correspond to periods when inflow to the lake was probably at extremes (e.g. drought or flood) indicating that fluctuations in river inflow may be an important factor affecting sediment composition in Pyramid Lake.
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    URL: http://dx.doi.org/10.1007/BF00678089
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  • 12
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    Thek-server dual and loose competitiveness for paging (1994)
    Springer
    Algorithmica 11 (1994), S. 525-541 
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    ISSN: 1432-0541
    Keywords: On-line algorithms ; k-Server problem ; Linear programming ; Approximation algorithms ; Paging ; Caching ; Competitive analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Weighted caching is a generalization ofpaging in which the cost to evict an item depends on the item. We study both of these problems as restrictions of the well-knownk-server problem, which involves moving servers in a graph in response to requests so as to minimize the distance traveled. We give a deterministic on-line strategy for weighted caching that, on any sequence of requests, given a cache holdingk items, incurs a cost within a factor ofk/(k−h+1) of the minimum cost possible given a cache holdingh items. The strategy generalizes “least recently used,” one of the best paging strategies in practice. The analysis is a primal-dual analysis, the first for an on-line problem, exploiting the linear programming structure of thek-server problem. We introduceloose competitiveness, motivated by Sleator and Tarjan's complaint [ST] that the standard competitive ratios for paging strategies are too high. Ak-server strategy isloosely c(k)-competitive if, for any sequence, foralmost all k, the cost incurred by the strategy withk serverseither is no more thanc(k) times the minimum costor is insignificant. We show that certain paging strategies (including “least recently used,” and “first in first out”) that arek-competitive in the standard model are looselyc(k)-competitive providedc(k)/Ink→∞ and bothk/c(k) andc(k) are nondecreasing. We show that the marking algorithm, a randomized paging strategy that is Θ(Ink)-competitive in the standard model, is looselyc(k)-competitive providedk−2 In Ink→∞ and both 2 Ink−c(k) andc(k) are nondecreasing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189992
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  • 13
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    Polynomial algorithms for linear programming over the algebraic numbers (1994)
    Springer
    Algorithmica 12 (1994), S. 436-457 
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    ISSN: 1432-0541
    Keywords: Linear programming ; Algebraic numbers ; Computational complexity ; Ellipsoid method ; Polynomial-time algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We derive a bound on the computational complexity of linear programs whose coefficients are real algebraic numbers. Key to this result is a notion of problem size that is analogous in function to the binary size of a rational-number problem. We also view the coefficients of a linear program as members of a finite algebraic extension of the rational numbers. The degree of this extension is an upper bound on the degree of any algebraic number that can occur during the course of the algorithm, and in this sense can be viewed as a supplementary measure of problem dimension. Working under an arithmetic model of computation, and making use of a tool for obtaining upper and lower bounds on polynomial functions of algebraic numbers, we derive an algorithm based on the ellipsoid method that runs in time bounded by a polynomial in the dimension, degree, and size of the linear program. Similar results hold under a rational number model of computation, given a suitable binary encoding of the problem input.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01188714
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  • 14
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    Linkages between organic matter mineralization and denitrification in eight riparian wetlands (1994)
    Springer
    Biogeochemistry 25 (1994), S. 19-39 
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    ISSN: 1573-515X
    Keywords: denitrification ; mineralization ; nitrification ; nitrogen ; riparian ; stream ; wetland ; New Jersey ; Pennsylvania ; Pinelands
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Denitrification (N2 production) and oxygen consumption rates were measured at ambient field nitrate concentrations during summer in sediments from eight wetlands (mixed hardwood swamps, cedar swamps, heath dominated shrub wetland, herbaceous peatland, and a wetland lacking live vegetation) and two streams. The study sites included wetlands in undisturbed watersheds and in watersheds with considerable agricultural and/or sewage treatment effluent input. Denitrification rates measured in intact cores of water-saturated sediment ranged from ≤ 20 to 260 μmol N m-2 h-1 among the three undisturbed wetlands and were less variable (180 to 260 μmol N M-2 h-1) among the four disturbed wetlands. Denitrification rates increased when nitrate concentrations in the overlying water were increased experimentally (1 up to 770 μM), indicating that nitrate was an important factor controlling denitrification rates. However, rates of nitrate uptake from the overlying water were not a good predictor of denitrification rates because nitrification in the sediments also supplied nitrate for denitrification. Regardless of the dominant vegetation, pH, or degree of disturbance, denitrification rates were best correlated with sediment oxygen consumption rates (r 2 = 0.912) indicating a relationship between denitrification and organic matter mineralization and/or sediment nitrification rates. Rates of denitrification in the wetland sediments were similar to those in adjacent stream sediments. Rates of denitrification in these wetlands were within the range of rates previously reported for water-saturated wetland sediments and flooded soils using whole core15N techniques that quantify coupled nitrification/denitrification, and were higher than rates reported from aerobic (non-saturated) wetland sediments using acetylene block methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00000510
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  • 15
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    The effects of flow rate and distance travelled on the mobility of phosphate in soils (1994)
    Springer
    Transport in porous media 16 (1994), S. 237-251 
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    ISSN: 1573-1634
    Keywords: phosphate ; soil ; adsorption ; leaching ; kinetics ; computer simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Effects of flow rate and distance travelled on average mobilities of phosphate in a soil are estimated from breakthrough curves of phosphate at the outlets of small columns of soil, following step increases in the concentration at the inlets. Experimental results are compared with results from a computer simulation model of leached columns of soil. Average mobilities of phosphate in columns of soil, following a step increase in the input concentration, decrease with decreasing rate of flow and with increasing distance travelled and appear to be linearly correlated on a logarithmic scale with both flow rate and distance travelled. An empirical equation, describing these relationships, is fitted to data from leaching experiments at flow rates between 30 and 600 cm/day in ≈ 10 cm long columns of soil. Coefficients are obtained by curve fitting breakthrough curves, calculated with a numerical computer simulation model, to experimental breakthrough curves. The fitted equation enables extrapolation to flow rates and travel distances that are more relevant to a field situation.
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    URL: http://dx.doi.org/10.1007/BF00617149
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  • 16
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    Linear programming formulation of MDPs in countable state space: The multichain case (1994)
    Springer
    Mathematical methods of operations research 40 (1994), S. 91-108 
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    ISSN: 1432-5217
    Keywords: Markov decision processes ; countable state space ; Linear programming ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We present an Linear Programming formulation of MDPs with countable state and action spaces and no unichain assumption. This is an extension of the Hordijk and Kallenberg (1979) formulation in finite state and action spaces. We provide sufficient conditions for both existence of optimal solutions to the primal LP program and absence of duality gap. Then, existence of a (possibly randomized) average optimal policy is also guaranteed. Existence of a stationary average optimal deterministic policy is also investigated.
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    URL: http://dx.doi.org/10.1007/BF01414031
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  • 17
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    Geometry of optimal value functions with applications to redundancy in linear programming (1994)
    Springer
    Journal of optimization theory and applications 81 (1994), S. 35-52 
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    ISSN: 1573-2878
    Keywords: Linear programming ; optimal value functions ; redundancy in linear programming ; convex hull problem ; data envelopment analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In 1967, Wets and Witzgall (Ref. 1) made, in passing, a connection between frames of polyhedral cones and redundancy in linear programming. The present work elaborates and formalizes the theoretical details needed to establish this relation. We study the properties of optimal value functions in order to derive the correspondence between problems in redundancy and the frame of a polyhedral cone. The insights obtained lead to schemes to improve the efficiency of procedures to detect redundancy in the areas of linear programming, stochastic programming, and computational geometry.
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    URL: http://dx.doi.org/10.1007/BF02190312
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  • 18
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    The simplex method as a global optimizer: A c-programming perspective (1994)
    Springer
    Journal of global optimization 4 (1994), S. 89-109 
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    ISSN: 1573-2916
    Keywords: Linear programming ; simplex method ; c-programming ; composite functions ; global optimization ; dc problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we give a brief account of the important role that the conventional simplex method of linear programming can play in global optimization, focusing on its collaboration with composite concave programming techniques. In particular, we demonstrate how rich and powerful the c-programming format is in cases where its parametric problem is a standard linear programming problem.
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    URL: http://dx.doi.org/10.1007/BF01096536
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  • 19
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    On solution-containing ellipsoids in linear programming (1994)
    Springer
    Journal of optimization theory and applications 80 (1994), S. 161-173 
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    ISSN: 1573-2878
    Keywords: Linear programming ; interior point methods ; containing ellipsoids ; optimal basic and nonbasic variables
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Ellipsoids that contain all optimal dual slack solutions and those that contain all optimal primal solutions and that are independent of the algorithm used are derived. Based upon these ellipsoids, two criteria each for detecting optimal basic and nonbasic variables prior to optimality in interior-point methods are obtained. Using these results, we then derive a sufficient condition for a linear program to be feasible.
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    URL: http://dx.doi.org/10.1007/BF02196599
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  • 20
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    Rank-one techniques in log-barrier function methods for linear programming (1994)
    Springer
    Journal of optimization theory and applications 82 (1994), S. 405-413 
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    ISSN: 1573-2878
    Keywords: Linear programming ; interior-point methods ; Karmarkar's method ; log-barrier function ; rank-one techniques ; computational complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This short paper presents a primal interior-point method for linear programming. The method can be viewed as a modification of the methods developed in Refs. 1–6. In each iteration, it computes an approximately projected Newton direction and needsO(n 2.5) arithmetic operations to make the log-barrier function significantly decrease. It requires $$O(\sqrt {nL} )$$ iterations, so that the total complexity isO(n 3 L).
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    URL: http://dx.doi.org/10.1007/BF02191863
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  • 21
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    Primal-dual algorithms for linear programming based on the logarithmic barrier method (1994)
    Springer
    Journal of optimization theory and applications 83 (1994), S. 1-26 
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    ISSN: 1573-2878
    Keywords: Linear programming ; primal-dual interior point methods ; logarithmic barrier function ; polynomial algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we deal with primal-dual interior point methods for solving the linear programming problem. We present a short-step and a long-step path-following primal-dual method and derive polynomial-time bounds for both methods. The iteration bounds are as usual in the existing literature, namely $$O(\sqrt n L)$$ iterations for the short-step variant andO(nL) for the long-step variant. In the analysis of both variants, we use a new proximity measure, which is closely related to the Euclidean norm of the scaled search direction vectors. The analysis of the long-step method depends strongly on the fact that the usual search directions form a descent direction for the so-called primal-dual logarithmic barrier function.
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    URL: http://dx.doi.org/10.1007/BF02191759
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    Near boundary behavior of primal—dual potential reduction algorithms for linear programming (1993)
    Springer
    Mathematical programming 58 (1993), S. 243-255 
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    ISSN: 1436-4646
    Keywords: Linear programming ; interior point algorithm ; primal—dual potential function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper is concerned with selection of theρ-parameter in the primal—dual potential reduction algorithm for linear programming. Chosen from [n + $$\sqrt n $$ , ∞), the level ofρ determines the relative importance placed on the centering vs. the Newton directions. Intuitively, it would seem that as the iterate drifts away from the central path towards the boundary of the positive orthant,ρ must be set close ton + $$\sqrt n $$ . This increases the relative importance of the centering direction and thus helps to ensure polynomial convergence. In this paper, we show that this is unnecessary. We find for any iterate thatρ can be sometimes chosen in a wide range [n + $$\sqrt n $$ , ∞) while still guaranteeing the currently best convergence rate of O( $$\sqrt n $$ L) iterations. This finding is encouraging since in practice large values ofρ have resulted in fast convergence rates. Our finding partially complements the recent result of Zhang, Tapia and Dennis (1990) concerning the local convergence rate of the algorithm.
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    URL: http://dx.doi.org/10.1007/BF01581269
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  • 23
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    Combining phase I and phase II in a potential reduction algorithm for linear programming (1993)
    Springer
    Mathematical programming 59 (1993), S. 133-150 
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    ISSN: 1436-4646
    Keywords: Linear programming ; interior-point methods ; combined phase I—phase II
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes an affine potential reduction algorithm for linear programming that simultaneously seeks feasibility and optimality. The algorithm is closely related to a similar method of Anstreicher. The new features are that we use a two-dimensional programming problem to derive better lower bounds than Anstreicher, that our direction-finding subproblem treats phase I and phase II more symmetrically, and that we do not need an initial lower bound. Our method also allows for the generation of a feasible solution (so that phase I is terminated) during the course of the iterations, and we describe two ways to encourage this behavior.
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    A quadratically convergent O( $$\sqrt n $$ L)-iteration algorithm for linear programming (1993)
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    Mathematical programming 59 (1993), S. 151-162 
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    ISSN: 1436-4646
    Keywords: Linear programming ; primal and dual ; superlinear and quadratic convergence ; polynomiality
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    Notes: Abstract Recently, Ye, Tapia and Zhang (1991) demonstrated that Mizuno—Todd—Ye's predictor—corrector interior-point algorithm for linear programming maintains the O( $$\sqrt n $$ L)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap to zero under the assumption of nondegeneracy. In this paper we establish the quadratic convergence result without any assumption concerning the convergence of the iteration sequence or nondegeneracy. This surprising result, to our knowledge, is the first instance of a demonstration of polynomiality and superlinear (or quadratic) convergence for an interior-point algorithm which does not assume the convergence of the iteration sequence or nondegeneracy.
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    A note on the prize collecting traveling salesman problem (1993)
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    Mathematical programming 59 (1993), S. 413-420 
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    ISSN: 1436-4646
    Keywords: Linear programming ; prize collecting ; rounding fractional solutions ; traveling salesman problem ; worst-case analysis
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    Notes: Abstract We study the version of the prize collecting traveling salesman problem, where the objective is to find a tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. We present an approximation algorithm with constant bound. The algorithm is based on Christofides' algorithm for the traveling salesman problem as well as a method to round fractional solutions of a linear programming relaxation to integers, feasible for the original problem.
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    Strict monotonicity and improved complexity in the standard form projective algorithm for linear programming (1993)
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    Mathematical programming 62 (1993), S. 517-535 
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    ISSN: 1436-4646
    Keywords: Linear programming ; Karmarkar's algorithm ; Projective algorithm ; Standard form
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    Notes: Abstract In a recent paper, Shaw and Goldfarb show that a version of the standard form projective algorithm can achieve $$O\left( {\sqrt {nL} } \right)$$ step complexity, as opposed to the O(nL) step complexity originally demonstrated for the algorithm. The analysis of Shaw and Goldfarb shows that the algorithm, using a constant, fixed steplength, approximately follows the central trajectory. In this paper we show that simple modifications of the projective algorithm obtain the same complexity improvement, while permitting a linesearch of the potential function on each step. An essential component is the addition of a single constraint, motivated by Shaw and Goldfarb's analysis, which makes the standard form algorithm strictly monotone in the true objective.
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    Determination of optimal vertices from feasible solutions in unimodular linear programming (1993)
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    Mathematical programming 59 (1993), S. 23-31 
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    ISSN: 1436-4646
    Keywords: Linear programming ; duality theorem ; unimodular ; totally unimodular ; interior point methods
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    Notes: Abstract In this paper we consider a linear programming problem with the underlying matrix unimodular, and the other data integer. Given arbitrary near optimum feasible solutions to the primal and the dual problems, we obtain conditions under which statements can be made about the value of certain variables in optimal vertices. Such results have applications to the problem of determining the stopping criterion in interior point methods like the primal—dual affine scaling method and the path following methods for linear programming.
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    A strictly improving linear programming Phase I algorithm (1993)
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    Annals of operations research 46-47 (1993), S. 409-430 
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    ISSN: 1572-9338
    Keywords: Linear programming ; Phase I ; nonlinear programming ; least squares ; quadratic programming ; strict improvement ; degeneracy
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    Topics: Mathematics , Economics
    Notes: Abstract Instead of trying to recognize and avoid degenerate steps in the simplex method (as some variants do), we have developed a new Phase I algorithm that is impervious to degeneracy. The new algorithm solves a non-negative least-squares problem in order to find a Phase I solution. In each iteration, a simple two-variable least-squares subproblem is used to select an incoming column to augment a set of independent columns (called “basic”) to get a strictly better fit to the right-hand side. Although this is analogous in many ways to the simplex method, it can be proved that strict improvement is attained at each iteration, even in the presence of degeneracy. Thus cycling cannot occur, and convergence is guaranteed. This algorithm is closely related to a number of existing algorithms proposed for non-negative least-squares and quadratic programs. When used on the 30 smallest NETLIB linear programming test problems, the computational results for the new Phase I algorithm were almost 3.5 times faster than a particular implementation of the simplex method; on some problems, it was over 10 times faster. Best results were generally seen on the more degenerate problems.
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    Degeneracy in interior point methods for linear programming: a survey (1993)
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    Annals of operations research 46-47 (1993), S. 107-138 
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    ISSN: 1572-9338
    Keywords: Linear programming ; interior point methods ; degeneracy ; polynomial algorithms ; global and local convergence ; basis recovery ; numerical performance ; sensitivity analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The publication of Karmarkar's paper has resulted in intense research activity into Interior Point Methods (IPMs) for linear programming. Degeneracy is present in most real-life problems and has always been an important issue in linear programming, especially in the Simplex method. Degeneracy is also an important issue in IPMs. However, the difficulties are different in the two methods. In this paper, we survey the various theoretical and practical issues related to degeneracy in IPMs for linear programming. We survey results, which, for the most part, have already appeared in the literature. Roughly speaking, we shall deal with the effect of degeneracy on the following: the convergence of IPMs, the trajectories followed by the algorithms, numerical performance, and finding basic solutions.
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    Studies of lexicography in the generalized network simplex method (1993)
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    Annals of operations research 46-47 (1993), S. 235-248 
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    ISSN: 1572-9338
    Keywords: Linear programming ; generalized networks ; simplex method ; degeneracy ; lexicography ; cycling
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    Topics: Mathematics , Economics
    Notes: Abstract This paper introduces an analytical approach for studying lexicography in generalized network problems. The equations obtained can help us to understand and to extend the existing theory. First, it is verified that all nonzero elements have the same sign in each row vector of a basis inverse for a generalized network (GN) problem with positive multipliers. However, this property does not necessarily hold when there exist negative multipliers. Second, we developed a strategy to select the dropping arc in the GN simplex algorithm when addressing GN problems with positive andnegative multipliers. This strategy is also based on lexicography and requires performing some comparisons. However, the values to be compared are already known since they can be obtained as a by-product of the calculations necessary to compute the basis representation of the entering arc. Consequently, the computational effort per pivot step isO(n) in the worst case. This worst case effort is the same as that required by the strongly convergent rules for selecting the dropping arc in the method of strong convergence.
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    Pivot rules for linear programming: A survey on recent theoretical developments (1993)
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    Annals of operations research 46-47 (1993), S. 203-233 
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    ISSN: 1572-9338
    Keywords: Linear programming ; simplex method ; pivot rules ; cycling ; recursion ; minimal index rule ; parametric programming
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    Topics: Mathematics , Economics
    Notes: Abstract The purpose of this paper is to discuss the various pivot rules of the simplex method and its variants that have been developed in the last two decades, starting from the appearance of the minimal index rule of Bland. We are mainly concerned with finiteness properties of simplex type pivot rules. Well known classical results concerning the simplex method are not considered in this survey, but the connection between the new pivot methods and the classical ones, if there is any, is discussed. In this paper we discuss three classes of recently developed pivot rules for linear programming. The first and largest class is the class of essentially combinatorial pivot rules including minimal index type rules and recursive rules. These rules only use labeling and signs of the variables. The second class contains those pivot rules which can actually be considered as variants or generalizations or specializations of Lemke's method, and so they are closely related to parametric programming. The last class has the common feature that the rules all have close connections to certain interior point methods. Finally, we mention some open problems for future research.
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    A practical anti-degeneracy row selection technique in network linear programming (1993)
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    Annals of operations research 46-47 (1993), S. 431-442 
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    ISSN: 1572-9338
    Keywords: Linear programming ; degeneracy ; network simplex algorithm ; pivoting ; minimal cost network flow
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    Topics: Mathematics , Economics
    Notes: Abstract A characteristic feature of the primal network simplex algorithm (NSA) is that it usually makes a large number of degenerate iterations. Though cycling and even stalling can be avoided by recently introduced pivot rules for NSA, the practical efficiency of these rules is not known yet. For the case when the simplex algorithm is used to solve the continuous linear programming (LP) problem there exists a practical anti-cycling procedure that proved to be efficient. It is based on an expanding relaxation of the individual bound on the variables. In this paper we discuss the adaptation of this method to NSA, taking advantage of the special integer nature of network problems. We also give an account of our experience with these ideas as they are experimentally implemented in the MINET network LP solver. Reductions of CPU time have been achieved on a smaller set of specially structured real-life problems.
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    An active-set strategy in an interior point method for linear programming (1993)
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    Mathematical programming 59 (1993), S. 345-360 
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    Keywords: Linear programming ; interior point method ; active set strategy
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    Notes: Abstract We will present a potential reduction method for linear programming where only the constraints with relatively small dual slacks—termed “active constraints”—will be taken into account to form the ellipsoid constraint at each iteration of the process. The algorithm converges to the optimal feasible solution in O( $$\sqrt n $$ L) iterations with the same polynomial bound as in the full constraints case, wheren is the number of variables andL is the data length. If a small portion of the constraints is active near the optimal solution, the computational cost to find the next direction of movement in one iteration may be considerably reduced by the proposed strategy.
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    A randomized scheme for speeding up algorithms for linear and convex programming problems with high constraints-to-variables ratio (1993)
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    Mathematical programming 61 (1993), S. 39-52 
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    ISSN: 1436-4646
    Keywords: Linear programming ; quadratic programming ; convex programming ; randomized algorithms ; fixed dimension optimization problems ; complexity
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    Notes: Abstract We extend Clarkson's randomized algorithm for linear programming to a general scheme for solving convex optimization problems. The scheme can be used to speed up existing algorithms on problems which have many more constraints than variables. In particular, we give a randomized algorithm for solving convex quadratic and linear programs, which uses that scheme together with a variant of Karmarkar's interior point method. For problems withn constraints,d variables, and input lengthL, ifn = Ω(d 2), the expected total number of major Karmarkar's iterations is O(d 2(logn)L), compared to the best known deterministic bound of O( $$\sqrt n$$ L). We also present several other results which follow from the general scheme.
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    Load balancing in the parallel optimization of block-angular linear programs (1993)
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    Mathematical programming 62 (1993), S. 41-67 
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    Keywords: Linear programming ; Dantzig—Wolfe decomposition ; large-scale systems ; parallel processing ; hypercube architecture
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    Notes: Abstract Decomposition algorithms for block-angular linear programs give rise to a natural, coarse-grained parallelism that can be exploited by processing the subproblems concurrently within a distributed-memory environment. The parallel efficiency of the distributed approach, however, is critically dependent on the duration of the inherently serial master phase relative to that of the bottleneck subproblem. This paper investigates strategies for improving efficiency in distributed Dantzig—Wolfe decomposition by better balancing the load between the master and subproblem processors. We report computational experience on an Intel iPSC/2 hypercube multiprocessor with test problems having dimensions up to about 30 000 rows, 87 000 columns, and 200 coupling constraints.
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    Solving symmetric indefinite systems in an interior-point method for linear programming (1993)
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    Mathematical programming 62 (1993), S. 15-39 
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    ISSN: 1436-4646
    Keywords: Linear programming ; interior-point methods ; symmetric indefinite systems
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    Notes: Abstract We describe an implementation of a primal—dual path following method for linear programming that solves symmetric indefinite “augmented” systems directly by Bunch—Parlett factorization, rather than reducing these systems to the positive definite “normal equations” that are solved by Cholesky factorization in many existing implementations. The augmented system approach is seen to avoid difficulties of numerical instability and inefficiency associated with free variables and with dense columns in the normal equations approach. Solving the indefinite systems does incur an extra overhead, whose median is about 40% in our tests; but the augmented system approach proves to be faster for a minority of cases in which the normal equations have relatively dense Cholesky factors. A detailed analysis shows that the augmented system factorization is reliable over a fairly large range of the parameter settings that control the tradeoff between sparsity and numerical stability.
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    A primal—dual affine-scaling potential-reduction algorithm for linear programming (1993)
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    Mathematical programming 62 (1993), S. 119-131 
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    ISSN: 1436-4646
    Keywords: Linear programming ; interior point algorithm ; complexity ; potential function
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    Notes: Abstract We propose a potential-reduction algorithm which always uses the primal—dual affine-scaling direction as a search direction. We choose a step size at each iteration of the algorithm such that the potential function does not increase, so that we can take a longer step size than the minimizing point of the potential function. We show that the algorithm is polynomial-time bounded. We also propose a low-complexity algorithm, in which the centering direction is used whenever an iterate is far from the path of centers.
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    Finding an interior point in the optimal face of linear programs (1993)
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    Mathematical programming 62 (1993), S. 497-515 
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    Keywords: Linear programming ; primal—dual methods ; optimal face ; strict complementarity
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    Notes: Abstract We study the problem of finding a point in the relative interior of the optimal face of a linear program. We prove that in the worst case such a point can be obtained in O(n 3 L) arithmetic operations. This complexity is the same as the complexity for solving a linear program. We also show how to find such a point in practice. We report and discuss computational results obtained for the linear programming problems in the NETLIB test set.
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    On combined phase 1-phase 2 projective methods for linear programming (1993)
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    Algorithmica 9 (1993), S. 64-83 
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    ISSN: 1432-0541
    Keywords: Linear programming ; Interior-point methods ; Projective methods ; Combined phase 1-phase 2
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    Notes: Abstract We compare the projective methods for linear programming due to de Ghellinck and Vial, Anstreicher, Todd, and Fraley. These algorithms have the feature that they approach feasibility and optimality simultaneously, rather than requiring an initial feasible point. We compare the directions used in these methods and the lower-bound updates employed. In many cases the directions coincide and two of the lower-bound updates give the same result. It appears that Todd's direction and Fraley's lower-bound update have slight advantages, and this is borne out in limited computational testing.
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    On partial updating in a potential reduction linear programming algorithm of Kojima, Mizuno, and Yoshise (1993)
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    Algorithmica 9 (1993), S. 184-197 
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    ISSN: 1432-0541
    Keywords: Linear programming ; Karmarkar's algorithm ; Potential function ; Primal-dual, Modified method ; Rank-one updates
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    Notes: Abstract We consider partial updating in Kojima, Mizuno, and Yoshise's primal-dual potential reduction algorithm for linear programming. We use a simple safeguard condition to control the number of updates incurred on combined primal-dual steps. Our analysis allows for unequal steplengths in the primal and dual variables, which appears to be a computationally significant factor for primal-dual methods. The safeguard we use is a primal-dual Goldstein-Armijo condition, modified to deal with the unequal primal and dual steplengths.
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    Simulated effects of precipitation and nitrogen on Serengeti grassland productivity (1993)
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    Biogeochemistry 22 (1993), S. 157-178 
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    ISSN: 1573-515X
    Keywords: Serengeti ; productivity ; precipitation ; nitrogen ; grazing
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    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract In the Serengeti National Park, Tanzania, precipitation and soil nitrogen vary greatly between northwestern tallgrass areas and southeastern shortgrass areas, with the tallgrass having higher total precipitation and lower soil fertility. We used a model of grassland productivity, carbon/nitrogen cycling, and abiotic factors to test the hypothesis that tallgrass productivity is limited primarily by nitrogen availability while shortgrass productivity is limited by water. Under observed grazing intensities and ungrazed conditions, precipitation exerted primary control over grassland productivity for both regions, with differences in soil texture mediating soil water availability to the grasses. Mineral nitrogen availability interacted with water availability to influence productivity at precipitation levels ⩾ 130% of the mean. Nitrogen mineralization and precipitation were positively related for each grassland type, however, nitrification varied both between grassland types and between grazed and ungrazed conditions. Combined mineralization and nitrification could not maintain soil mineral nitrogen levels in the face of plant nitrogen uptake stimulated by increased precipitation, thus providing the mechanism by which nitrogen becomes a secondary limiting factor for both grasslands. Model experiments indicated that the pattern of primary limitation by precipitation and secondary limitation by nitrogen was robust to model assumptions concerning ungulate deposition of urine and dung nitrogen to the soil.
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    Mass loss and nitrogen dynamics in decomposing acid forest litter in the Netherlands at increased nitrogen deposition (1993)
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    Biogeochemistry 20 (1993), S. 45-62 
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    ISSN: 1573-515X
    Keywords: atmospheric deposition ; forest ecosystems ; litter decomposition ; The Netherlands ; nitrogen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Litterbag experiments were carried out in five forest ecosystems in the Netherlands to study weight loss and nitrogen dynamics during the first two years of decomposition of leaf and needle litter. All forests were characterized by a relatively high atmospheric nitrogen input by throughfall, ranging from 22–55 kg N ha−1 yr−1. Correlation analysis of all seven leaf and needle litters revealed no significant relation between the measured litter quality indices (nitrogen and lignin concentration, lignin-to-nitrogen ratio) and the decomposition rate. A significant linear relation was found between initial lignin-to-nitrogen ratio and critical nitrogen concentration, suggesting an effect of litter quality on nitrogen dynamics. Comparison of the decomposition of oak leaves in a nitrogen-limited and a nitrogen-saturated forest suggested an increased nitrogen availability. The differences in capacities to retain atmospheric nitrogen inputs between these two sites could be explained by differences in net nitrogen immobilization in first year decomposing oak leaves: in the nitrogen-limited oak forest a major part (55%) of the nitrogen input by throughfall was immobilized in the first year oak leaf litter. The three coniferous forests consisted of two monocultures of Douglas fir and a mixed stand of Douglas fir and Scots pine. Despite comparable litter quality in the Douglas fir needles in all sites, completely different nitrogen dynamics were found.
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    Nutrient limitations to plant growth during primary succession in Hawaii Volcanoes National Park (1993)
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    Biogeochemistry 23 (1993), S. 197-215 
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    ISSN: 1573-515X
    Keywords: chronosequence ; montane tropical forest ; nitrogen ; soil development ; phosphorus ; tropical forest
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract We determined the effects of nutrient amendments on plant growth in three tropical montane rainforest sites representing a sequence of soil ages (〈 30, 200, and ≈ 2000 y). Factorial fertilization with nitrogen, phosphorus, and all other essential nutrients (combined) was applied to the two younger sites; only nitrogen was applied to the oldest one. Nitrogen supply represented the most important limitation to plant growth in the two younger sites; additions of nitrogen caused significant increases in tree diameter increment, height growth, litterfall, and most other growth-related parameters. In contrast, nitrogen additions had no significant effect on plant growth in the oldest site. Phosphorus additions increased extractable soil phosphorus and plant tissue phosphorus, but did not increase plant growth at the young sites. The results are consistent with Walker & Syers' (1976) model for the control of nutrient limitation during soil development.
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    Long steps in an O(n 3 L) algorithm for linear programming (1992)
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    Mathematical programming 54 (1992), S. 251-265 
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    ISSN: 1436-4646
    Keywords: Linear programming ; Karmarkar's algorithm ; potential function ; standard form ; modified method ; rank-one updates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider partial updating in Ye's affine potential reduction algorithm for linear programming. We show that using a Goldstein—Armijo rule to safeguard a linesearch of the potential function during primal steps is sufficient to control the number of updates. We also generalize the dual step construction to apply with partial updating. The result is the first O(n 3 L) algorithm for linear programming whose steps are not constrained by the need to remain approximately centered. The fact that the algorithm has a rigorous “primal-only” initialization actually reduces the complexity to less than O(m 1.5 n 1.5 L).
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    On Anstreicher's combined phase I—phase II projective algorithm for linear programming (1992)
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    Mathematical programming 55 (1992), S. 1-15 
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    ISSN: 1436-4646
    Keywords: Linear programming ; interior-point method ; projective algorithm ; combining phase I–phase II
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    Notes: Abstract Anstreicher has proposed a variant of Karmarkar's projective algorithm that handles standard-form linear programming problems nicely. We suggest modifications to his method that we suspect will lead to better search directions and a more useful algorithm. Much of the analysis depends on a two-constraint linear programming problem that is a relaxation of the scaled original problem.
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    Zur Modellierung logischer Aussagen ergänzend zu Linearen Programmen (1992)
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    OR spectrum 14 (1992), S. 149-160 
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    ISSN: 1436-6304
    Keywords: Lineare Programmierung ; logische Aussagen ; Binärvariablen ; Modellgenerator ; Linear programming ; predicates ; binary variables ; model generator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary We introduce in the field of formulating logical predicates in addition to linear programs. The error prone process of developing linear constraints including binary variables (“auxilliary formulations”) to accomplish this leads us to discuss the possibilities and capabilities of model generation. Based on Williams [12] we develop the formulae apparatus and discuss formulation and design problems for the development of our model generator now being implemented.
    Notes: Zusammenfassung Wir geben eine Einführung in das Gebiet der Formulierung logischer Aussagen ergänzend zu Linearen Programmen. Der dazu notwendige, fehlerträchtige Prozeß der Aufstellung linearer Restriktionen unter der Verwendung von Binärvariablen („Ersatzformulierungen“) führt uns dazu, die Möglichkeiten und Fähigkeiten eines Modellgenerators für diesen Zweck zu diskutieren. Auf der Grundlage von Williams [12] entwickeln wir den Formelapparat und erörtern Formulierungs- und Entwurfsprobleme für die Entwicklung unseres sich jetzt in der Implementationsphase befindlichen Modellgenerators.
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    Polynomial algorithms for LP over a subring of the algebraic integers with applications to LP with circulant matrices (1992)
    Springer
    Mathematical programming 57 (1992), S. 121-143 
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    ISSN: 1436-4646
    Keywords: Linear programming ; polynomial-time algorithms ; strongly polynomial-time algorithms ; circulant matrices ; algebraic numbers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that a modified variant of the interior point method can solve linear programs (LPs) whose coefficients are real numbers from a subring of the algebraic integers. By defining the encoding size of such numbers to be the bit size of the integers that represent them in the subring, we prove the modified algorithm runs in time polynomial in the encoding size of the input coefficients, the dimension of the problem, and the order of the subring. We then extend the Tardos scheme to our case, obtaining a running time which is independent of the objective and right-hand side data. As a consequence of these results, we are able to show that LPs with real circulant coefficient matrices can be solved in strongly polynomial time. Finally, we show how the algorithm can be applied to LPs whose coefficients belong to the extension of the integers by a fixed set of square roots.
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    MODLER: Modeling by object-driven linear elemental relations (1992)
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    Annals of operations research 38 (1992), S. 239-280 
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    ISSN: 1572-9338
    Keywords: Linear programming ; large-scale systems ; modeling ; language design
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper describes a system to represent linear programming models and their instances. In addition to a modeling language, MODLER has an extensive query capability which includes a multi-view architecture. Further, randomization options provide rapid prototyping. The MODLER system is part of a workbench for building and managing decision support systems that are based on linear programming.
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    A simplex algorithm for piecewise-linear programming III: Computational analysis and applications (1992)
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    Mathematical programming 53 (1992), S. 213-235 
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    ISSN: 1436-4646
    Keywords: Linear programming ; simplex methods ; piecewise-linear programming ; nondifferentiable optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The first two parts of this paper have developed a simplex algorithm for minimizing convex separable piecewise-linear functions subject to linear constraints. This concluding part argues that a direct piecewiselinear simplex implementation has inherent advantages over an indirect approach that relies on transformation to a linear program. The advantages are shown to be implicit in relationships between the linear and piecewise-linear algorithms, and to be independent of many details of implementation. Two sets of computational results serve to illustarate these arguments; the piecewise-linear simplex algorithm is observed to run 2–6 times faster than a comparable linear algorithm, not including any additional expense that might be incurred in setting up the equivalent linear program. Further support for the practical value of a good piecewise-linear programming algorithm is provided by a survey of many varied applications.
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    Finding effective “force targets” for two-dimensional, multifinger frictional grips (1992)
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    Algorithmica 8 (1992), S. 1-20 
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    ISSN: 1432-0541
    Keywords: Robotics ; Grasp planning ; Robot control ; Computational Geometry ; Linear programming ; Parametric searching ; Davenport-Schinzel sequences
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we apply techniques from computational geometry to solve several problems in grasp planning and control in robotics. We consider the problem of calculating “force targets ” for a collection ofn fingers which grasp a two-dimensional object at known positions, at which the normals to the surface are also assumed to be known at least approximately. If the points at which the fingers touch the body do not allow apositive grip to be exerted (i.e., a grip in which the fingers hold the body in equilibrium by exerting friction-free forces in the directions of the corresponding inward-directed normals), it is appropriate to find the smallest coefficient of friction for which it is possible to assign a set of forces to be exerted by the fingers (so-calledfinger-force targets) which hold the object at equilibrium and such that each individual force lies within the corresponding cone of friction. We present an algorithm for this problem which runs in time0(n log2 n log logn). We also present another algorithm for preprocessing the given data so as to allow fast computation of the desired coefficient of friction for the case in which one needs to balance any given “query” external force and torque. Finally, we discuss simpler variants of our techniques which are likely to be more efficient when the problem is solved for a small number of fingers.
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    A geometric view of parametric linear programming (1992)
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    Algorithmica 8 (1992), S. 161-176 
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    ISSN: 1432-0541
    Keywords: Parametric linear programming ; Sensitivity analysis ; Postoptimality analysis ; Linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a new definition of optimality intervals for the parametric right-hand side linear programming (parametric RHS LP) Problem ϑ(λ) = min{c t x¦Ax =b + λ¯b,x ≥ 0}. We then show that an optimality interval consists either of a breakpoint or the open interval between two consecutive breakpoints of the continuous piecewise linear convex function ϑ(λ). As a consequence, the optimality intervals form a partition of the closed interval {λ; ¦ϑ(λ)¦ 〈 ∞}. Based on these optimality intervals, we also introduce an algorithm for solving the parametric RHS LP problem which requires an LP solver as a subroutine. If a polynomial-time LP solver is used to implement this subroutine, we obtain a substantial improvement on the complexity of those parametric RHS LP instances which exhibit degeneracy. When the number of breakpoints of ϑ(λ) is polynomial in terms of the size of the parametric problem, we show that the latter can be solved in polynomial time.
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    A projection and contraction method for a class of linear complementarity problems and its application in convex quadratic programming (1992)
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    Applied mathematics & optimization 25 (1992), S. 247-262 
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    ISSN: 1432-0606
    Keywords: Projection ; Féjer-contraction ; Linear complementarity problem ; Linear programming ; Convex quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we propose a new iterative method for solving a class of linear complementarity problems:u ≥ 0,Mu + q ≥ 0, uT(Mu + q)=0, where M is a givenl ×l positive semidefinite matrix (not necessarily symmetric) andq is a givenl-vector. The method makes two matrix-vector multiplications and a trivial projection onto the nonnegative orthant at each iteration, and the Euclidean distance of the iterates to the solution set monotonously converges to zero. The main advantages of the method presented are its simplicity, robustness, and ability to handle large problems with any start point. It is pointed out that the method may be used to solve general convex quadratic programming problems. Preliminary numerical experiments indicate that this method may be very efficient for large sparse problems.
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    Exchange of N2O and CH4 between the atmosphere and soils in spruce-fir forests in the northeastern United States (1992)
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    Biogeochemistry 18 (1992), S. 119-135 
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    ISSN: 1573-515X
    Keywords: N2O ; CH4 ; red spruce ; balsam fir ; spruce-fir ; forests ; nitrogen ; deposition ; nitrification ; mineralization ; denitrification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract We measured the exchange of N2O and CH4 between the atmosphere and soils in 5 spruce-fir stands located along a transect from New York to Maine. Nitrous oxide emissions averaged over the 1990 growing season (May–September) ranged from 2.1 ug N2O-N/m2-hr in New York to 0.4 ug N2O-N/m2-hr in Maine. The westernmost sites, Whiteface Mtn., New York and Mt. Mansfield, Vermont, had the highest nitrogen-deposition, net nitrification and N2O emissions. Soils at all sites were net sinks for atmospheric CH4 Methane uptake averaged over the 1990 growing season ranged from 0.02 mg CH4-C/M2-hr in Maine to 0.05 mg CH4-C/m2-hr in Vermont. Regional differences in CH4 uptake could not be explained by differences in nitrogen-deposition, soil nitrogen dynamics, soil moisture or soil temperature. We estimate that soils in spruce-fir forests at our study sites released ca. 0.02 to 0.08 kg N2O-N/ha and consumed ca. 0.74 to 1.85 kg CH4 C/ha in the 1990 growing season.
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    Nitrogen immobilization in leaf litter at two Mediterranean ecosystems of SW Spain (1992)
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    Biogeochemistry 15 (1992), S. 213-228 
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    ISSN: 1573-515X
    Keywords: immobilization ; leaf litter decomposition ; lignin ; Mediterranean ecosystem ; nitrogen ; tannin
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Nitrogen immobilization in relation to the dynamics of lignin and tannins in nine different types of leaf litter was investigated during a 2-yr study at two Mediterranean ecosystems of SW Spain. Net nitrogen immobilization for all the species was higher in a forest than in the more nutrient-poor soil of a shrubland. Absolute amount of lignin increased in both ecosystems in the first 2–4 months whereas tannin rapidly decreased in the same time period. Increases in lignin were significantly correlated to losses of tannins during decomposition. Initial tannin content was the best predictor of the maximum amount of immobilized nitrogen in litter in both ecosystems. Mechanisms that could explain the immobilization of nitrogen in litter are discussed.
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    Effects of nitrogen: phosphorus supply ratios on nitrogen fixation in agricultural and pastoral ecosystems (1992)
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    Biogeochemistry 18 (1992), S. 19-35 
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    ISSN: 1573-515X
    Keywords: Dinitrogen fixation ; nitrogen ; phosphorus ; competition ; legumes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract An analysis of data compiled from the literature confirms a strong inverse relationship between annual rates of nitrogen fixation and the soil nitrogen content in agricultural and pastoral ecosystems. However, this inverse relationship is strongly modified by the rate of application of phosphorus fertilizer, which strongly influences the activities of both symbiotic and non-symbiotic nitrogen fixing organisms. In the case of symbiotic legumes, the response of N-fixation to N and P is in part a result of changes in legume dominance within the plant community. These results, as well as supporting data presented from a review of experiments on nitrogen fixation in a variety of other terrestrial and aquatic ecosystems, provide important support for the hypothesis that phosphorus availability is a key regulator of nitrogen biogeochemistry.
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    Carbon and nitrogen limitations of soil microbial biomass in desert ecosystems (1992)
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    Biogeochemistry 18 (1992), S. 1-17 
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    ISSN: 1573-515X
    Keywords: microbial biomass-N ; desert ; carbon ; nitrogen ; shrubland ; grassland ; playa
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Microbial biomass nitrogen was measured in unamended (dry) and wetted soils in ten shrubland and grassland communities of the Chihuahuan desert, southern New Mexico, by the fumigation-extraction method. Microbial biomass-N in dry soils was undetectable. Average microbial biomass-N in wetted soils among all plant communities was 15.3 μg g-1 soil. Highest values were found in the communities with the lowest topographic positions, and the minimum values were detected in the spaces between shrubs. Microbial biomass was positively and significantly correlated to soil organic carbon and extractable nitrogen (NH4 + + NO3 -). In a stepwise multiple regression, organic carbon and extractable nitrogen accounted for 40.9 and 5.6%, respectively, of the variance in microbial biomass-N among all the samples. Among communities, the soil microbial biomass was affected by the ratio of carbon to extractable nitrogen. Our results suggest a succession in the control of microbial biomass from nitrogen to carbon when the ratio of carbon to nitrogen decreases during desertification.
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    Soil nutrient dynamics in response to irrigation of a Panamanian tropical moist forest (1992)
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    Biogeochemistry 19 (1992), S. 1-25 
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    ISSN: 1573-515X
    Keywords: nitrogen ; phosphorus ; soil fertility ; tropical forest
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract We measured concentrations of soil nutrients (0–15 and 30–35 cm depths) before and after the dry season in control and dry-season irrigated plots of mature tropical moist forest on Barro Colorado Island (BCI) in central Panama to determine how soil moisture affects availability of plant nutrients. Dry-season irrigation (January through April in 1986, 1987, and 1988) enhanced gravimetric soil water contents to wet-season levels (ca. 400 g kg−1 but did not cause leaching beyond 0.8 m depth in the soil. Irrigation increased concentrations of exchangeable base cations (Ca2+, Mg2+, K+, Na+), but it had little effect on concentrations of inorganic N (NH4 +C, NO3 − and S (SO4 2−). These BCI soils had particularly low concentrations of extractable P especially at the end of the dry season in April, and concentrations increased in response to irrigation and the onset of the rainy season. We also measured the response of soil processes (nitrification and S mineralization) to irrigation and found that they responded positively to increased soil moisture in laboratory incubations, but irrigation had little effect on rates in the field. Other processes (plant uptake, soil organic matter dynamics) must compensate in the field and keep soil nutrient concentrations at relatively low levels.
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    L 1 Sensitivity minimization for plants with commensurate delays (1992)
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    Mathematics of control, signals, and systems 5 (1992), S. 281-293 
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    ISSN: 1435-568X
    Keywords: L 1 optimal control ; Delay and infinite-dimensional linear systems ; Linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics , Technology
    Notes: Abstract In this paper we consider the problem ofL 1 sensitivity minimization for linear plants with commensurate input delays. We describe a procedure for computing the minimum performance, and we characterize optimal solutions. The computations involve solving a one-parameter family of finite-dimensional linear programs. Explicit solutions are presented for important special cases.
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    Stoichiometric relationships among producers, consumers and nutrient cycling in pelagic ecosystems (1992)
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    Biogeochemistry 17 (1992), S. 49-67 
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    ISSN: 1573-515X
    Keywords: algae ; nitrogen ; nutrient ; phosphorus ; regeneration ; zooplankton
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Most ecosystem models consolidate members of food-webs, e.g. species, into a small number of functional components. Each of these is then described by a single state variable such as biomass. When a multivariate approach incorporating multiple substances within components is substituted for this univariate one, a ‘stoichiometric’ model is formed. Here we show that the Nitrogen:Phosphorus ratio within zooplankton herbivores varies substantially intraspecifically but not intraspecifically. By using stoichiometric theory and recent measurements of the N:P ratio within different zooplankton taxa, we calculate large differences in ratios of nutrients recycled by different zooplankton species. Finally, we demonstrate that N:P stoichiometry can successfully account for shifts in N- and P-limitation previously observed in whole-lake experiments. Species stoichiometry merges food-web dynamics with biogeochemical cycles to yield new insights.
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    Superlinear and quadratic convergence of primal-dual interior-point methods for linear programming revisited (1992)
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    Journal of optimization theory and applications 73 (1992), S. 229-242 
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    ISSN: 1573-2878
    Keywords: Linear programming ; primal-dual interior-point algorithms ; superlinear convergence ; quadratic convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently, Zhang, Tapia, and Dennis (Ref. 1) produced a superlinear and quadratic convergence theory for the duality gap sequence in primal-dual interior-point methods for linear programming. In this theory, a basic assumption for superlinear convergence is the convergence of the iteration sequence; and a basic assumption for quadratic convergence is nondegeneracy. Several recent research projects have either used or built on this theory under one or both of the above-mentioned assumptions. In this paper, we remove both assumptions from the Zhang-Tapia-Dennis theory.
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    Sensitivity method for basis inverse representation in multistage stochastic linear programming problems (1992)
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    Journal of optimization theory and applications 74 (1992), S. 221-242 
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    ISSN: 1573-2878
    Keywords: Linear programming ; stochastic programming ; simplex method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A version of the simplex method for solving stochastic linear control problems is presented. The method uses a compact basis inverse representation that extensively exploits the original problem data and takes advantage of the supersparse structure of the problem. Computational experience indicates that the method is capable of solving large problems.
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    An unconstrained convex programming view of linear programming (1992)
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    Mathematical methods of operations research 36 (1992), S. 149-161 
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    ISSN: 1432-5217
    Keywords: Linear programming ; Barrier Function ; Entropy Function ; Geometric Programming ; Convex programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The major interest of this paper is to show that, at least in theory, a pair of primal and dual “ɛ-optimal solutions” to a general linear program in Karmarkar's standard form can be obtained by solving an unconstrained convex program. Hence unconstrained convex optimization methods are suggested to be carefully reviewed for this purpose.
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    Interior proximal point algorithm for linear programs (1992)
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    Journal of optimization theory and applications 74 (1992), S. 425-444 
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    ISSN: 1573-2878
    Keywords: Linear programming ; interior point method ; proximal point method ; Newton method
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    Topics: Mathematics
    Notes: Abstract An interior proximal point algorithm for finding a solution of a linear program is presented. The distinguishing feature of this algorithm is the addition of a quadratic proximal term to the linear objective function. This perturbation has allowed us to obtain solutions with better feasibility. Implementation of this algorithm shows that the algorithms. We also establish global convergence and local linear convergence of the algorithm.
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    Deriving an unconstrained convex program for linear programming (1992)
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    Journal of optimization theory and applications 75 (1992), S. 603-612 
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    ISSN: 1573-2878
    Keywords: Linear programming ; convex programming ; geometric programming ; duality theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Consider a linear programming problem in Karmarkar's standard form. By perturbing its linear objective function with an entropic barrier function and applying generalized geometric programming theory to it, Fang recently proposed an unconstrained convex programming approach to finding an epsilon-optimal solution. In this paper, we show that Fang's derivation of an unconstrained convex dual program can be greatly simplified by using only one simple geometric inequality. In addition, a system of nonlinear equations, which leads to a pair of primal and dual epsilon-optimal solutions, is proposed for further investigation.
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    Extensions of the potential reduction algorithm for linear programming (1992)
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    Journal of optimization theory and applications 72 (1992), S. 487-498 
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    ISSN: 1573-2878
    Keywords: Linear programming ; primal and dual problems ; bimatrix games ; potential function ; potential reduction algorithm
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    Topics: Mathematics
    Notes: Abstract In this work, we study several extensions of the potential reduction algorithm that was developed for linear programming. These extensions include choosing different potential functions, generating the analytic center of a polytope, and finding the equilibrium of a zero-sum bimatrix game.
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    Comparative analysis of affine scaling algorithms based on simplifying assumptions (1991)
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    Mathematical programming 52 (1991), S. 405-414 
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    ISSN: 1436-4646
    Keywords: Linear programming ; primal and dual ; potential reduction algorithm ; affine scaling algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We analyze several affine potential reduction algorithms for linear programming based on simplifying assumptions. We show that, under a strong probabilistic assumption regarding the distribution of the data in an iteration, the decrease in the primal potential function will be $$\Omega (\rho /\sqrt {log(n)} )$$ with high probability, compared to the guaranteedΩ(1). (ρ ⩾2n is a parameter in the potential function andn is the number of variables.) Under the same assumption, we further show that the objective reduction rate of Dikin's affine scaling algorithm is $$(1 - 1/\sqrt {log(n)} )$$ with high probability, compared to no guaranteed convergence rate.
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    Global convergence of the affine scaling methods for degenerate linear programming problems (1991)
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    Mathematical programming 52 (1991), S. 377-404 
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    ISSN: 1436-4646
    Keywords: Linear programming ; interior point methods ; affine scaling methods ; global analysis ; degenerate problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we show the global convergence of the affine scaling methods without assuming any condition on degeneracy. The behavior of the method near degenerate faces is analyzed in detail on the basis of the equivalence between the affine scaling methods for homogeneous LP problems and Karmarkar's method. It is shown that the step-size 1/8, where the displacement vector is normalized with respect to the distance in the scaled space, is sufficient to guarantee the global convergence of the affine scaling methods.
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    A combined phase I—phase II scaled potential algorithm for linear programming (1991)
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    Mathematical programming 52 (1991), S. 429-439 
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    ISSN: 1436-4646
    Keywords: Linear programming ; potential function ; phase I ; phase II ; artificial variable
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    Notes: Abstract We develop an extension of the affinely scaled potential reduction algorithm which simultaneously obtains feasibility and optimality in a standard form linear program, without the addition of any “M” terms. The method, and its lower-bounding procedure, are particularly simple compared with previous interior algorithms not requiring feasibility.
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    An O(n 3 L) adaptive path following algorithm for a linear complementarity problem (1991)
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    Mathematical programming 52 (1991), S. 587-595 
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    ISSN: 1436-4646
    Keywords: Linear programming ; linear complementarity problem ; interior point algorithms ; path following algorithms
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    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we propose an O(n 3 L) algorithm which is a modification of the path following algorithm [8] for a linear complementarity problem. The path following algorithm has to take a short step size in each iteration in order to bound the number of overall arithmetic operations by O(n 3 L). In practical computation, we can determine the step size adaptively. Mizuno, Yoshise, and Kikuchi [11] reported that such an adaptive algorithm required about O(L) iterations for some test problems. Here we show that we can use a rank one update technique in the adaptive algorithm so that the number of overall arithmetic operations is theoretically bounded by O(n 3 L).
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    Linear programming with spheres and hemispheres of objective vectors (1991)
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    Mathematical programming 51 (1991), S. 1-16 
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    ISSN: 1436-4646
    Keywords: Linear programming ; parametric ; homeomorphisms ; spheres ; hemispheres
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Given a linear program with a boundedp-dimensional feasible region let the objective vector range over ans-sphere, that is, ans-dimensional sphere centered at the origin wheres does not exceedp−1. If the feasible region and the sphere are in general position with respect to each other, then the corresponding set of all optimal solutions is a topologicals-sphere. Similar results are developed for unbounded feasible regions and hemispheres of objective vectors.
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    An O(n 3 L) potential reduction algorithm for linear programming (1991)
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    Mathematical programming 50 (1991), S. 239-258 
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    ISSN: 1436-4646
    Keywords: Linear programming ; primal and dual ; interior algorithms ; potential functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe a primal-dual potential function for linear programming: $$\phi (x,s) = \rho \ln (x^T s) - \sum\limits_{j = 1}^n {\ln (x_j s_j )} $$ whereρ⩾ n, x is the primal variable, ands is the dual-slack variable. As a result, we develop an interior point algorithm seeking reductions in the potential function with $$\rho = n + \sqrt n $$ . Neither tracing the central path nor using the projective transformation, the algorithm converges to the optimal solution set in $$O(\sqrt n L)$$ iterations and uses O(n 3 L) total arithmetic operations. We also suggest a practical approach to implementing the algorithm.
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    Improving the rate of convergence of interior point methods for linear programming (1991)
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    Mathematical programming 52 (1991), S. 467-479 
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    ISSN: 1436-4646
    Keywords: Linear programming ; polynomial methods ; interior point methods ; rate of convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper proposes a procedure for improving the rate of convergence of interior point methods for linear programming. If (x k ) is the sequence generated by an interior point method, the procedure derives an auxiliary sequence ( $$\bar x^k$$ ). Under the suitable assumptions it is shown that the sequence ( $$\bar x^k$$ ) converges superlinearly faster to the solution than (x k ). Application of the procedure to the projective and afflne scaling algorithms is discussed and some computational illustration is provided.
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    Search directions for interior linear-programming methods (1991)
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    Algorithmica 6 (1991), S. 153-181 
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    ISSN: 1432-0541
    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 Since Karmarkar published his algorithm for linear programming, several different interior directions have been proposed and much effort was spent on the problem transformations needed to apply these new techniques. This paper examines several search directions in a common framework that does not need any problem transformation. These directions prove to be combinations of two problem-dependent vectors, and can all be improved by a bidirectional search procedure. We conclude that there are essentially two polynomial algorithms: Karmarkar's method and the algorithm that follows a central trajectory, and they differ only in a choice of parameters (respectively lower bound and penalty multiplier).
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    URL: http://dx.doi.org/10.1007/BF01759039
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    Retiming synchronous circuitry (1991)
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    Algorithmica 6 (1991), S. 5-35 
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    ISSN: 1432-0541
    Keywords: Digital circuitry ; Graph theory ; Linear programming ; Network flow ; Optimization ; Pipelining ; Propagation delay ; Retiming ; Synchronous circuitry ; Systolic circuits ; Timing analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes a circuit transformation calledretiming in which registers are added at some points in a circuit and removed from others in such a way that the functional behavior of the circuit as a whole is preserved. We show that retiming can be used to transform a given synchronous circuit into a more efficient circuit under a variety of different cost criteria. We model a circuit as a graph in which the vertex setV is a collection of combinational logic elements and the edge setE is the set of interconnections, each of which may pass through zero or more registers. We give anO(¦V∥E¦lg¦V¦) algorithm for determining an equivalent retimed circuit with the smallest possible clock period. We show that the problem of determining an equivalent retimed circuit with minimum state (total number of registers) is polynomial-time solvable. This result yields a polynomial-time optimal solution to the problem of pipelining combinational circuitry with minimum register cost. We also give a chacterization of optimal retiming based on an efficiently solvable mixed-integer linear-programming problem.
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    Inverse methods and kinetic models of hydrocarbon generation: III. Case histories for autoclave product analysis (1991)
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    Mathematical geology 23 (1991), S. 325-347 
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    ISSN: 1573-8868
    Keywords: hydrocarbons ; kinetics ; inverse methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract From a determination of the transformation matrix for three pyrolysis product experimental data sets, an examination is given of both the applicability of the laboratory experimental data to the modeling of oil cracking in a sedimentary basin, and of the appropriateness of an inverse model. The results of the laboratory experimental data sets, which were done under different thermodynamic conditions and using different sources, show that the transformation matrix varies over each data set and also with time. Therefore, it is necessary to check the data sets before applying them to a basin for hydrocarbon modeling. The laboratory experimental data taken at lower temperature and over longer times appear more pertinent for the construction of an oil-cracking kinetic model suitable for geologic conditions.
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    Combustion losses of sulphur from conifer foliage: Implications of chemical form and soil nitrogen status (1991)
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    Biogeochemistry 12 (1991), S. 129-134 
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    ISSN: 1573-515X
    Keywords: biomass burning ; forest soils ; nitrogen ; sulphur
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract The proportion of total sulphur lost during combustion (600 °C) of Douglas-fir (Pseudotsuga menziesii) foliage is reduced from〉 90% to 65–70% as the SO4-S concentration increases from 10% to 45–50% of the total S content. Foliar SO4-S content is decreased by improvement of plant nitrogen status, suggesting that alterations to soil N availability may influence S transfer to the atmosphere during biomass burning.
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    Nitrogen cycling in an acid forest ecosystem in the Netherlands under increased atmospheric nitrogen input (1991)
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    Biogeochemistry 15 (1991), S. 21-46 
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    ISSN: 1573-515X
    Keywords: denitrification ; forest ; nitrification ; nitrogen ; nitrogen mineralization ; N20 ; proton budget ; The Netherlands
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Within a long-term research project studying the biogeochemical budget of an oak-beech forest ecosystem in the eastern part of the Netherlands, the nitrogen transformations and solute fluxes were determined in order to trace the fate of atmospherically deposited NH4 + and to determine the contribution of nitrogen transformations to soil acidification. The oak-beech forest studied received an annual input of nitrogen via throughfall and stemflow of 45 kg N ha−1 yr−1, mainly as NH4 +, whereas 8 kg N ha−1 yr−1 was taken up by the canopy. Due to the specific hydrological regime resulting in periodically occurring high groundwater levels, denitrification was found to be the dominant output flux (35 kg N ha−1 yr−1). N20 emmission rate measurements indicated that 57% of this gaseous nitrogen loss (20 kg N ha−1 yr−1) was as N2O. The forest lost an annual amount of 11 kg N ha−1 yr−1 via streamwater output, mainly as N03 −. Despite the acid conditions, high nitrification rates were measured. Nitrification occurred mainly in the litter layer and in the organic rich part of the mineral soil and was found to be closely correlated with soil temperature. The large amount of NH4 + deposited on the forest floor via atmospheric deposition and produced by mineralization was to a large extent nitrified in the litter layer. Almost no NH4 + reached the subsurface soil horizons. The N03 − was retained, taken up or transformed mainly in the mineral soil. A small amount of N03 − (9 kg N ha−1 yr−1) was removed from the system in streamwater output. A relatively small amount of nitrogen was measured in the soil water as Dissolved Organic Nitrogen. On the basis of these data the proton budget of the system was calculated using two different approaches. In both cases net proton production rates were high in the vegetation and in the litter layer of the forest ecosystem. Nitrogen transformations induced a net proton production rate of 2.4 kmol ha−1 yr−1 in the soil compartment.
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    Control of plant growth by nitrogen and phosphorus in mesotrophic fens (1991)
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    Biogeochemistry 12 (1991), S. 135-148 
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    ISSN: 1573-515X
    Keywords: fens ; management ; nitrogen ; phosphorus ; productivity ; vegetation ; wetlands
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract A fertilization experiment was carried out in 3 mesotrophic fens to investigate whether plant growth in these systems is controlled by the availability of N, P or K. The fens are located in an area with high N inputs from precipitation. They are annually mown in the summer to prevent succession to woodland. Above-ground plant biomass increased significantly upon N fertilization in the two “mid”-succession fens studied. In the “late”-succession fen that had been mown for at least 60 years, however, plant biomass increased significantly upon P fertilization. The mowing regime depletes the P pool in the soil, while it keeps N inputs and outputs in balance. A long-term shift occurs from limitation of plant production by N toward limitation by P. Hence, mowing is a suitable management tool to conserve the mesothrophic character of the fens.
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    Nitrogen deposition, distribution and cycling in a subalpine spruce-fir forest in the Adirondacks, New York, USA (1991)
    Springer
    Biogeochemistry 14 (1991), S. 31-55 
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    ISSN: 1573-515X
    Keywords: atmospheric deposition ; nitrogen ; nutrient cycling ; spruce decline ; subalpine spruce-fir
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Nitrogen inputs, fluxes, internal generation and consumption, and outputs were monitored in a subalpine spruce-fir forest at approximately 1000-m elevation on Whiteface Mountain in the Adirondacks of New York, USA. Nitrogen in precipitation, cloudwater and dry deposition was collected on an event basis and quantified as an input. Throughfall, stemflow, litterfall and soil water were measured to determine fluxes within the forest. Nitrogen mineralization in the forest floor was estimated to determine internal sources of available N. Lower mineral horizon soil water was used to estimate output from the ecosystem. Vegetation and soil N pools were determined. During four years of continuous monitoring, an average of 16 kg N ha−1 yr−1 was delivered to the forest canopy as precipitation, cloudwater and dry deposition from the atmosphere. Approximately 30% of the input was retained by the canopy. Canopy retention is likely the result of both foliar uptake and immobilization by bark, foliage and microorganisms. Approximately 40 kg of N was made available within the forest floor from mineralization of organic matter. Virtually all the available ammonium (mineralized plus input from throughfall) is utilized in the forest floor, either by microorganisms or through uptake by vegetation. The most abundant N component of soil water solutions leaving the system was nitrate. Net ecosystem fluxes indicate accumulation of both ammonium and nitrate. There is a small net loss of organic N from the ecosystem. Some nitrate leaves the bottom of the B horizon throughout the year. Comparisons with other temperate coniferous sites and examination of the ecosystem N mass balance indicate that N use efficiency is less at our site, which suggests that the site is not severely limited by N.
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    An experimental technique for studying heterogeneous reactions of polyaromatic hydrocarbons on particle surfaces (1991)
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    Journal of atmospheric chemistry 12 (1991), S. 137-151 
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    ISSN: 1573-0662
    Keywords: Soot particles ; polycyclic aromatic hydrocarbons ; NO2 ; HNO3 ; heterogeneous reactions ; kinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract An experimental technique for studying atmospheric heterogeneous reactions of polyaromatic hydrocarbons (PAH) on particle surfaces is reported. Particle bound organics were reacted in a 200 liter Teflon continuous stirred tank reactor (CSTR), with vapor phase oxidants. To provide a source of chemically stable particles for the CSTR, soot particles from a residential wood stove were first introduced during under darkness into a 25 m3 outdoor Teflon chamber. Air containing the particles was then added at a constant flow to the CSTR. The rates of heterogeneous reactions were obtained by comparing reacted particle samples with unreacted ones. The derivation of rate expressions for heterogeneous reactions in the CSTR is described. The use of the technique for a study of the nitration of selected soot particle bound PAH species by NO2 and HNO3 is demonstrated.
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    Relative-rate study of the gas-phase reaction of hydroxy radicals with difunctional organic nitrates at 298 K and atmospheric pressure (1991)
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    Journal of atmospheric chemistry 13 (1991), S. 301-311 
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    ISSN: 1573-0662
    Keywords: Organic nitrates ; kinetics ; OH radical ; atmosphere
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Rate coefficients for the reactions of difunctional nitrates with atmospherically important OH radicals are not currently available in the literature. This study represents the first determination of rate coefficients for a number of C(3) and C(4) carbonyl nitrates and dinitrates with OH radicals in a 38 l glass reaction chamber at 1000 mbar total pressure of synthetic air by 298±2 K using a relative kinetic technique. The following rate coefficients (in units of 10-12 cm3 molecule-1 s-1) were obtained: 1,2-propandiol dinitrate, 〈0.31; 1,2-butandiol dinitrate, 1.70±0.32; 2,3-butandiol dinitrate, 1.07±0.26; α-nitrooxyacetone, 〈0.43; 1-nitrooxy-2-butanone, 0.91±0.16; 3-nitrooxy-2-butanone, 1.27±0.14; 1,4-dinitrooxy-2-butene, 15.10±1.45; 3,4-dinitrooxy-1-butene, 10.10±0.50. The possible importance of reaction of OH as an atmospheric sink for the compounds compared to other loss processes is considered.
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    Linear programming by minimizing distances (1991)
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    Mathematical methods of operations research 35 (1991), S. 299-307 
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    ISSN: 1432-5217
    Keywords: Linear programming ; Newton's method ; penalty methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract To solve the linear program (LP): minimizec T l subject toA l+b≥0, for ann×d-matrixA, ann-vectorb and ad-vectorc, the positive orthantS and the planeE(t) are defined by S={(x1,x)εℝn+1 ¦(x1,x)⩾0}, E(t)={(x1,x)εℝn+1¦x1=−c c l+t, x=Al+b}. First a geometric algorithm is given to determine d(E(t),S) for fixedt, where d(·,·) denotes euclidean distance. This algorithm is used to construct a second algorithm to find the minimalt with E(t) ∩S ≠ ∅, and thus solve LP. It is shown that all algorithms are finite.
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    Unrestricted variables in linear programming (1991)
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    Journal of optimization theory and applications 69 (1991), S. 605-610 
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    ISSN: 1573-2878
    Keywords: Linear programming ; unrestricted variables ; extreme points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract There are a number of ways of dealing with a linear programming problem in which some variables are allowed to take on negative values. One of these methods, which is either ignored or mentioned only incidentally in most textbooks, requires only one additional variable to be introduced regardless of how many unrestricted variables the original problem has. In this note, this method is interpreted geometrically and an application to the computation of extreme points is given.
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    Feasibility issues in a primal-dual interior-point method for linear programming (1990)
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    Mathematical programming 49 (1990), S. 145-162 
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    ISSN: 1436-4646
    Keywords: Linear programming ; interior-point methods ; primal—dual algorithms ; feasibility
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A new method for obtaining an initial feasible interior-point solution to a linear program is presented. This method avoids the use of a “big-M”, and is shown to work well on a standard set of test problems. Conditions are developed for obtaining a near-optimal solution that is feasible for an associated problem, and details of the computational testing are presented. Other issues related to obtaining and maintaining accurate feasible solutions to linear programs with an interior-point method are discussed. These issues are important to consider when solving problems that have no primal or dual interior-point feasible solutions.
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    A “build-down” scheme for linear programming (1990)
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    Mathematical programming 46 (1990), S. 61-72 
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    ISSN: 1436-4646
    Keywords: Linear programming ; simplex method ; ellipsoid method ; Karmarkar's algorithm ; primal and dual
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We propose a “build-down” scheme for Karmarkar's algorithm and the simplex method for linear programming. The scheme starts with an optimal basis “candidate” setΞ including all columns of the constraint matrix, then constructs a dual ellipsoid containing all optimal dual solutions. A pricing rule is developed for checking whether or not a dual hyperplane corresponding to a column intersects the containing ellipsoid. If the dual hyperplane has no intersection with the ellipsoid, its corresponding column will not appear in any of the optimal bases, and can be eliminated fromΞ. As these methods iterate,Ξ is eventually built-down to a set that contains only the optimal basic columns.
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    Polynomial affine algorithms for linear programming (1990)
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    Mathematical programming 49 (1990), S. 7-21 
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    ISSN: 1436-4646
    Keywords: Linear programming ; affine algorithms ; Karmarkar's algorithm ; interior methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The method of steepest descent with scaling (affine scaling) applied to the potential functionq logc′x — ∑ i=1 n logx i solves the linear programming problem in polynomial time forq ⩾ n. Ifq = n, then the algorithm terminates in no more than O(n 2 L) iterations; if q ⩾ n + $$\sqrt n $$ withq = O(n) then it takes no more than O(nL) iterations. A modified algorithm using rank-1 updates for matrix inversions achieves respectively O(n 4 L) and O(n 3.5 L) arithmetic computions.
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    On the improvement per iteration in Karmarkar's algorithm for linear programming (1990)
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    Mathematical programming 46 (1990), S. 299-320 
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    ISSN: 1436-4646
    Keywords: Linear programming ; Karmarkar ; projective ; potential
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We investigate the decrease in potential at an iteration of Karmarkar's projective method for linear programming. For a fixed step length parameterα (so that we must have 0 〈α ≤ 1) the best possible guaranteeδ n (α) inn dimensional space is essentially ln 2 ≃ 0.69; and to achieve this we must takeα about 1. Indeed we show the precise result thatδ n (α) equals ln(1 +α)-ln(1 −α/(n − 1)) forn sufficiently large. If we choose an optimal step length at each iteration then this guarantee increases only to aboutδ * ≃ 0.72. We also shed some light on the remarkable empirical observation that the number of iterations required seems scarcely to grow with the size of the problem.
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    An exponential example for Terlaky's pivoting rule for the criss-cross simplex method (1990)
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    Mathematical programming 46 (1990), S. 79-84 
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    ISSN: 1436-4646
    Keywords: Linear programming ; pivoting rule ; Gray code
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Recently T. Terlaky has proposed a new pivoting rule for the criss-cross simplex method for linear programming and he proved that his rule is convergent. In this note we show that the required number of iterations may be exponential in the number of variables and constraints of the problem.
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    Karmarkar's algorithm with improved steps (1990)
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    Mathematical programming 46 (1990), S. 73-78 
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    ISSN: 1436-4646
    Keywords: Linear programming ; Karmarkar's algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We define a function of the interior of the feasible region of Karmarkar's canonical linear program with the property that its supremum is bounded above by one, if and only if the optimal value of the linear program is zero. We use this function to obtain data-dependent steps for Karmarkar's algorithm. The corresponding reduction in the potential function improves upon the data-independent reduction derived by Padberg. We analyze the general step and consider its potential practical advantages.
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    Containing and shrinking ellipsoids in the path-following algorithm (1990)
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    Mathematical programming 47 (1990), S. 1-9 
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    ISSN: 1436-4646
    Keywords: Linear programming ; convex quadratic programming ; path-following algorithm ; Karmarkar's algorithm ; ellipsoid method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe a new potential function and a sequence of ellipsoids in the path-following algorithm for convex quadratic programming. Each ellipsoid in the sequence contains all of the optimal primal and dual slack vectors. Furthermore, the volumes of the ellipsoids shrink at the ratio $$2^{ - \Omega (\sqrt n )} $$ , in comparison to 2−Ω(1) in Karmarkar's algorithm and 2−Ω(1/n) in the ellipsoid method. We also show how to use these ellipsoids to identify the optimal basis in the course of the algorithm for linear programming.
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    A standard form variant, and safeguarded linesearch, for the modified Karmarkar algorithm (1990)
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    Mathematical programming 47 (1990), S. 337-351 
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    ISSN: 1436-4646
    Keywords: Linear programming ; Karmarkar's algorithm ; projective algorithm ; modified method ; standard form ; rank-one updates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In his original analysis of the projective algorithm for linear programming, Karmarkar proposed a “modified method” which improved the worst-case arithmetic complexity of the original algorithm by a factor of $$\sqrt n $$ . Karmarkar's analysis of the $$\sqrt n $$ improvement is based on a primal-dual formulation, and requires that small steps be taken on each iteration. However, in practice the original algorithm can be easily applied to standard form problems, and is considerably improved by performing a linesearch on each iteration, generally leading to much larger steps. We show here that by incorporating a simple safeguard, a linesearch may be performed in the modified algorithm while retaining the $$\sqrt n $$ complexity improvement over the original algorithm. We then show that the modified algorithm, with safeguarded linesearch, can be applied directly to a standard form linear program with unknown optimal objective value. The resulting algorithm enjoys a $$\sqrt n $$ complexity advantage over standard form variants of the original algorithm.
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    Factors affecting sulfur incorporation into lake sediments: paleoecological implications (1990)
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    Journal of paleolimnology 4 (1990), S. 1-22 
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    ISSN: 1573-0417
    Keywords: sulfate ; carbon ; nitrogen ; hydrogen ; organic matter ; enrichment factor ; lake sediments ; paleolimnology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences
    Notes: Abstract This paper discusses the use of S as a paleolimnological tracer of limnetic sulfate concentration. A positive relationship (p〈0.05) was found between limnetic sulfate and sediment S concentrations for the Great Lakes, English Lakes, and lakes from the Adirondack and Northern New England regions. There is a positive correlation (p〈0.05) between C and S concentration in sediment across all regions studied. The importance of C in affecting S content in sediment was also examined by a series of cores taken at different water depths in Big Moose Lake (Adirondacks). There was a strong relationship between C and S among cores with sediment from deeper water having higher C and S concentrations (r 2=0.99). Sulfur from the shallower cores had greater concentrations of chromium-reducible S (pyrite), while cores from deeper waters had a greater proportion of organic S fractions including C-bonded S and ester sulfates. For assessing historical changes in S accumulation in sediments, enrichment factors were calculated for the PIRLA lakes. Pre-1900 net sediment accumulation rates of S were very similar across all regions. Sulfur enrichment was greatest in Adirondack sediment which had total post-1900 S accumulation of 1.1 to 7.4 times pre-1900 S accumulation. Sediment from Northern New England (NNE) generally had lower S concentration than Adirondack sediments and S enrichment factors ranged from 1.2 to 2.1. Sediment from the Northern Great Lakes States region had similar S concentration and distribution with depth to NNE sediment. In two Northern Florida lakes, sediment showed little variation in S concentration with depth, but in two other lakes from the same region, there was higher S concentration in deeper layers. Lakes which had the greatest enrichment factors also exhibited the most marked changes in C:S ratios. Ratios of C:N showed little variation (10.6 to 26.1) among the PIRLA lakes. A first order model indicated slow decomposition within these organic rich sediments. Elemental concentrations and ratios of sediment from a variety of lakes and reservoirs were complied. Maximum and minimum elemental ratios for all the data were 28 to 8.1 for C:N, 0.81 to 0.11 for C:H, and 675 to 12.5 for C:S, respectively. For the C:S ratios in all regions except the Great Lakes, the maximum ratio was less than 231. Both the maximum and minimum amount of N and H concentration of organic matter is related to biotic processes. The minimum concentration of S is regulated not only by nutrient demands but also by non-assimilatory processes. Sulfur incorporation into sediments is a function of a complex of factors, but limnetic sulfate concentration and organic matter content play a major role in regulating the S content of sediment. Further quantification of S incorporation pathways will aid in the paleolimnological interpretation of sediment S profiles. Such information is also important in assessing how S sediment pools will respond to decreases in limnetic sulfate concentration which may occur with decreases in inputs from acidic deposition.
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    URL: http://dx.doi.org/10.1007/BF00208295
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  • 93
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    Nitrogen loss from deserts in the southwestern United States (1990)
    Springer
    Biogeochemistry 10 (1990), S. 67-79 
    Details
    ISSN: 1573-515X
    Keywords: deserts ; ecosystem ; nitrogen ; nutrient cycling ; soils ; southwestern United States
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract A lower limit for nitrogen loss from desert ecosystems in the southwestern United States was estimated by comparing nitrogen inputs to the amount of nitrogen stored in desert soils and vegetation. Atmospheric input of nitrogen for the last 10 000 years was conservatively estimated to be 2.99 kg N/m2. The amount of nitrogen stored in desert soils was calculated to be 0.604 kg N/m3 using extant data from 212 profiles located in Arizona, California, Nevada, and Utah. The average amount of nitrogen stored in desert vegetation is approximately 0.036 kg N/m2. Desert conditions have existed in the southwestern United States throughout the last 10 000 years. Under such conditions, vertical leaching of nitrogen below a depth of 1 m is small (ca. 0.028 kg N/m2 over 10 000 years) and streamflow losses of nitrogen from the desert landscape are negligible. Thus, the discrepancy found between nitrogen input and storage represents the amount of nitrogen lost to the atmosphere during the last 10 000 years. Loss of nitrogen to the atmosphere was calculated to be 2.32 kg N/m2, which is 77% of the atmospheric inputs. Processes resulting in nitrogen loss to the atmosphere from desert ecosystems include wind erosion, ammonia volatilization, nitrification, and denitrification. Our analysis cannot assess the relative importance of these processes, but each is worthy of future research efforts.
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    URL: http://dx.doi.org/10.1007/BF00000893
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  • 94
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    Landscape interactions among nitrogen mineralization, species composition, and long-term fire frequency (1990)
    Springer
    Biogeochemistry 11 (1990), S. 1-22 
    Details
    ISSN: 1573-515X
    Keywords: disturbance ; ecosystems ; forests ; indirect interactions ; landscape ecology ; Minnesota ; nitrogen ; nutrient cycling ; path analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Path analysis was used to determine the importance of long-term disturbance regime and the relative importances of correlations among vegetation patterns, disturbance history, and nitrogen (N) mineralization in old-growth forests of northwestern Minnesota. Leaf biomass (estimated by allometric equations), fire history (from fire scars on Pinus resinosa trees), and N mineralization rates (estimated from incubationsin situ) were determined from sample plots dominated by Betula papyrifera, Populus tremuloides, andP. grandidentata a mixture ofAcer saccharumandTilia americana, or Quercus borealis andOstrya virginiana. Results showed that topographic and soil-moisture controls on N mineralization, vegetation patterns, and disturbance are substantially stronger than is suggested by direct correlation. Indirect interactions among ecosystem variables played in important role. These interactions probably include the tendency for species that cycle large amounts of N to colonize more mesic sites that burned rarely in the past. Soil moisture was correlated both directly with N mineralization and indirectly, through its effects on vegetation pattern, and thus, litter quality. Although disturbance regime also depended on topography, the strengths of relationships between disturbance regime and other variables were relatively weak. These dependencies suggested that long-term fire regime is probably more a consequence than a cause for vegetation and fertility patterns. Topography, through its effects on soil moisture and microclimate, is an overriding influence on ecosystem properties, which in turn influence fire regime.
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    URL: http://dx.doi.org/10.1007/BF00000849
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  • 95
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    The cumulative effect of wetlands on stream water quality and quantity. A landscape approach (1990)
    Springer
    Biogeochemistry 10 (1990), S. 105-141 
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    ISSN: 1573-515X
    Keywords: cumulative ; flow ; GIS ; landscape ; lead ; nitrogen ; phosphorus ; suspended solids ; watershed ; wetlands
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract A method was developed to evaluate the cumulative effect of wetland mosaics in the landscape on stream water quality and quantity in the nine-county region surrounding Minneapolis—St. Paul, Minnesota. A Geographic Information System (GIS) was used to record and measure 33 watershed variables derived from historical aerial photos. These watershed variables were then reduced to eight principal components which explained 86% of the variance. Relationships between stream water quality variables and the three wetland-related principal components were explored through stepwise multiple regression analysis. The proximity of wetlands to the sampling station was related to principal component two, which was associated with decreased annual concentrations of inorganic suspended solids, fecal coliform, nitrates, specific conductivity, flow-weighted NH4 flow-weighted total P, and a decreased proportion of phosphorus in dissolved form(p 〈 0.05). Wetland extent was related to decreased specific conductivity, chloride, and lead concentrations. The wetland-related principal components were also associated with the seasonal export of organic matter, organic nitrogen, and orthophosphate. Relationships between water quality and wetlands components were different for time-weighted averages as compared to flow-weighted averages. This suggests that wetlands were more effective in removing suspended solids, total phosphorus, and ammonia during high flow periods but were more effective in removing nitrates during low flow periods.
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    URL: http://dx.doi.org/10.1007/BF00002226
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  • 96
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    The role of ammonium and nitrate retention in the acidification of lakes and forested catchments (1990)
    Springer
    Biogeochemistry 11 (1990), S. 23-43 
    Details
    ISSN: 1573-515X
    Keywords: acid precipitation ; ammonium ; mass balance ; nitrate ; nitrogen ; retention
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract The relative contribution of HN03 to precipitation acidity in eastern Canada has increased in recent years leading to some concern that the relative importance of NO− 3 deposition in acidification of terrestrial and aquatic ecosystems may increase. To gauge the extent of this impact, annual mass balances for N0− 3 and NH+ 4 were calculated for several forested catchments and lakes in Ontario. Retention of NH+ 4 (R NH4) by forested catchments was consistently high compared to retention of NO3 − (R NO3) which was highly variable. Retention of inorganic nitrogen was influenced by catchment grade and areal water discharge. In lakes, the reciprocals of retention of N0− 3 and NH+ 4 were linearly related to the ratio of lake mean depth to water residence time (z/τ; equal to areal water discharge), and retention did not appear to be a function of degree of acidification of the lakes. Net N consumption-based acidification of lakes, defined as the ratio of annual NH; mass to N0− 3 mass consumption, was negatively correlated with /τ and N consumption-related acidification was most likely to occur when − was 〈 1.5 m yr−1. If retention mechanisms are unaffected by changes in deposition, changes in deposition will still result in changes in surface water concentrations although the changes will be of similar proportions. Therefore, ‘NO− 3 saturation’ should not be defined by concentrations alone, but should be defined as decreasing long-term, average NO− 3 retention in streams and lakes in response to long-term increases in NO− 3 deposition. Analysis o f survey data will be facilitated by grouping lakes and catchments according to similar characteristics.
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    URL: http://dx.doi.org/10.1007/BF00000850
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  • 97
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    Nitrate concentrations in snow from remote areas: implication for the global NO x flux (1990)
    Springer
    Biogeochemistry 9 (1990), S. 211-222 
    Details
    ISSN: 1573-515X
    Keywords: nitrogen ; snow ; flux
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Increased emissions of nitrogen compounds to the atmosphere by human activities have been well documented. However, in order to better quantify these anthropogenic emissions, better knowledge of natural emissions rates must be known. In addition, variation in natural emissions through time should be documented. In this note we present data collected and/or analyzed by us for NO3 − in recent snow from remote regions of the world. We also summarize existing data sets from other remote regions. This is done to establish a better understanding of NO3 − deposition rates in these regions as well as to add more information to our global understanding of NO3 − deposition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00000599
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  • 98
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    Atmospheric input of inorganic nitrogen to the Western Mediterranean (1990)
    Springer
    Biogeochemistry 9 (1990), S. 117-134 
    Details
    ISSN: 1573-515X
    Keywords: nitrogen ; Mediterranean ; natural versus anthropogenic atmospheric nitrogen ; atmospheric input ; riverine input ; marine ecosystems ; primary production
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Bulk inorganic nitrogen deposition was monitored over a period of 3 years at the Bavella Pass (Corsica, France). Annual fluxes range between 126 and 150μmol.m−2.d-−1, increasing slightly with annual rainfall. Natural background average concentrations of rain water and associated fluxes were estimated from a classification of rain events into ‘natural’ (Oceanic and Saharan), polluted and composite. Long range transport of incoming polluted air masses increases the atmospheric wet nitrogen input by at least a factor of 1.6 in this Mediterranean area. Extrapolation of atmospheric dissolved inorganic nitrogen input to the Western Mediterranean leads to fluxes of 80 to l00μmol.m−2.d-−1. This atmospheric input is in the same order of magnitude as the inorganic nitrogen riverine input. As a consequence, the nitrogen budget for the Mediterranean has had to be reassessed. Atmospheric wet inorganic nitrogen input is of noticeable importance to marine Mediterranean ecosystems, representing on average 10 to 25% of new production in the Western Basin, with values of up to 60% in oligotrophic zones.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00692168
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  • 99
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    The heterogeneous formation of N2O in air containing NO2, O3 and NH3 (1990)
    Springer
    Journal of atmospheric chemistry 11 (1990), S. 255-269 
    Details
    ISSN: 1573-0662
    Keywords: NH3 ; NO2 ; O3 ; N2O formation ; kinetics ; nighttime NO2 oxidation ; heterogeneous reaction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract In a nighttime system and under relatively dry conditions (about 15 ppm H2O), the reaction mixture of NO2, O3, and NH3 in purified air turns out to result in the formation of nitrous oxide (N2O). The experiments were performed in a continuous stirred flow reactor, in the concentration region of 0.02–2 ppm. N2O is thought to arise through the heterogeneous reaction of gaseous N2O5 and absorbed NH3 at the wall of the reaction vessel % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9sq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9pue9Fve9% Ffc8meGabaqaciGacaGaaeqabaWaaeaaeaaakeaatCvAUfKttLeary% qr1ngBPrgaiuaacqWFOaakcqWFobGtcqWFibasdaWgaaWcbaGae83m% amdabeaakiab-LcaPmaaBaaaleaacqWFHbqyaeqaaOGaey4kaSIaai% ikaiab-5eaonaaBaaaleaacqWFYaGmaeqaaOGae83ta80aaSbaaSqa% aiab-vda1aqabaGccaGGPaWaaSbaaSqaaiaadEgaaeqaaOGaeyOKH4% Qae8Nta40aaSbaaSqaaiab-jdaYaqabaGccqWFpbWtcqGHRaWkcqWF% ibascqWFobGtcqWFpbWtdaWgaaWcbaGae83mamdabeaakiabgUcaRi% ab-HeainaaBaaaleaacqWFYaGmaeqaaOGae83ta8eaaa!59AC!\[(NH_3 )_a + (N_2 O_5 )_g \to N_2 O + HNO_3 + H_2 O\] In principle, there is competition between this reaction and that of adsorbed H2O with N2O5, resulting in the formation of HNO3. At high water concentrations (RH〉75%), no formation of N2O was found. Although the rate constant of adsorbed NH3 with gaseous N2O5 is much larger than that of the reaction of adsorbed H2O with gaseous N2O5, the significance of the observed N2O formation for the outside atmosphere is thought to be dependent on the adsorption properties of H2O and NH3 on a surface. A number of NH3 and H2O adsorption measurements on several materials are discussed.
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    URL: http://dx.doi.org/10.1007/BF00118352
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  • 100
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    Carbon and nitrogen cycling in North American boreal forests (1990)
    Springer
    Biogeochemistry 10 (1990), S. 1-28 
    Details
    ISSN: 1573-515X
    Keywords: boreal forest ; decomposition ; litter quality ; nitrogen ; productivity ; soil temperature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract A model of boreal forest dynamics was adapted to examine the factors controlling carbon and nitrogen cycling in the boreal forests of interior Alaska. Empirical relationships were used to simulate decomposition and nitrogen availability as a function of either substrate quality, the soil thermal regime, or their interactive effects. Test comparisons included black spruce forests growing on permafrost soils and black spruce, birch, and white spruce forests growing on permafrost-free soils. For each forest, simulated above-ground tree biomass, basal area, density, litterfall, moss biomass, and forest floor mass, turnover, thickness, and nitrogen concentration were compared to observed data. No one decay equation simulated forests entirely consistent with observed data, but over the range of upland forest types in interior Alaska, the equation that combined the effects of litter quality and the soil thermal regime simulated forests that were most consistent with observed data. For black spruce growing on permafrost soils, long-term simulated forest dynamics in the absence of fire resulted in unproductive forests with a thick forest floor and low nitrogen mineralization. Fires were an important means to interrupt this sequence and to restart forest succession.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00000889
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