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  • Books
  • Articles  (8)
  • linear programming
  • 1980-1984  (8)
  • Mathematics  (8)
  • 1
    Electronic Resource
    Electronic Resource
    Preface to topics in data envelopment analysis (1984)
    Springer
    Annals of operations research 2 (1984), S. 59-94 
    Details
    ISSN: 1572-9338
    Keywords: Efficiency ; Pareto optimality ; production functions ; returns to scale ; nondiscretionary inputs ; linear programming ; fractional programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper serves as an introduction to a series of three papers which are directed to different aspects of DEA (Data Envelopment Analysis) as follows: (1) uses and extensions of window analyses' to study DEA efficiency measures with an illustrative applications to maintenance activities for U.S. Air Force fighter wings, (2) a comparison of DEA and regression approaches to identifying and estimating, sources of inefficiency by means of artificially generated data, and (3) an extension of ordinary (linear programming) sensitivity analyses to deal with special features that require attention in DEA. Background is supplied in this introductory paper with accompanying proofs and explanations to facilitate understanding of what DEA provides in the way of underpinning for the papers that follow. An attempt is made to bring readers abreast of recent progress in DEA research and uses. A synoptic history is presented along with brief references to related work, and problems requiring attention are also indicated and possible research approaches also suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01874733
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  • 2
    Electronic Resource
    Electronic Resource
    Ranking of vertices in the linear fractional programming problem (1983)
    Springer
    BIT 23 (1983), S. 403-405 
    Details
    ISSN: 1572-9125
    Keywords: Vertex ranking ; fractional programming ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper the problem of ranking vertices in the linear fractional programming problem is considered. It is shown that a class of vertex ranking algorithms for the linear programming problem can be used with only minor modifications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01934470
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  • 3
    Electronic Resource
    Electronic Resource
    A method for stratigraphic correlation of several boreholes (1984)
    Springer
    Mathematical geology 16 (1984), S. 393-406 
    Details
    ISSN: 1573-8868
    Keywords: geophysical logs ; multivariate statistics ; cluster analysis ; linear programming ; dynamic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The borehole slotting method previously proposed by Gordon and Reyment for two boreholes may be extended to three or more boreholes, but soon becomes computationally intractable. We propose another method based on the mixture model of cluster analysis, the computational labor of which increases linearly with the number of boreholes. This method produces profiles of the unknown strata to which the individual boreholes are easily matched by the two-borehole slotting method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029888
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  • 4
    Electronic Resource
    Electronic Resource
    Inverse programming and the linear vector maximization problem (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 523-534 
    Details
    ISSN: 1573-2878
    Keywords: Vector maximization ; efficient vector ; optimal inverse apir ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a new concept of efficient solution for the linear vector maximization problem. Briefly, these solutions are efficient with respect to the constraints, in addition to being efficient with respect to the multiple objectives. The duality theory of linear vector maximization is developed in terms of this solution concept and then is used to formulate the problem as a linear program.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01686718
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  • 5
    Electronic Resource
    Electronic Resource
    Solution of nonlinear optimal control problems in Hilbert spaces by means of linear programming techniques (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 643-661 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; measures ; Hilbert spaces ; linear programming ; approximation techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Optimal control problems in Hilbert spaces are considered in a measure-theoretical framework. Instead of minimizing a functional defined on a class of admissible trajectory-control pairs, we minimize one defined on a set of measures; this set is defined by the boundary conditions and the differential equation of the problem. The new problem is an infinite-dimensionallinear programming problem; it is shown that it is possible to approximate its solution by that of a finite-dimensional linear program of sufficiently high dimensions, while this solution itself can be approximated by a trajectory-control pair. This pair may not be strictly admissible; if the dimensionality of the finite-dimensional linear program and the accuracy of the computations are high enough, the conditions of admissibility can be said to be satisfied up to any given accuracy. The value given by this pair to the functional measuring the performance criterion can be about equal to theglobal infimum associated with the classical problem, or it may be less than this number. It appears that this method may become a useful technique for the computation of optimal controls, provided the approximations involved are acceptable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01686727
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  • 6
    Electronic Resource
    Electronic Resource
    A note on Khatchian's algorithm (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 595-597 
    Details
    ISSN: 1573-2878
    Keywords: Khatchian's algorithm ; duality theorem ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A short proof of some properties of Khatchian's algorithm is presented using the duality theorem of linear programming.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934042
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  • 7
    Electronic Resource
    Electronic Resource
    Divisors of polynomials with positive coefficients (1980)
    Springer
    Periodica mathematica Hungarica 11 (1980), S. 117-130 
    Details
    ISSN: 1588-2829
    Keywords: Primary 26A78 ; Secondary 90C50 ; Positive polynomial ; location of zeros of polynomials ; linear programming ; finite cone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02017964
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  • 8
    Electronic Resource
    Electronic Resource
    A compact formulation of an elastoplastic analysis problem (1982)
    Springer
    Journal of optimization theory and applications 37 (1982), S. 343-353 
    Details
    ISSN: 1573-2878
    Keywords: Engineering plasticity ; elastoplastic analysis ; linear programming ; quadratic programming ; alternative optimal solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two important problems in the area of engineering plasticity are limit load analysis and elastoplastic analysis. It is well known that these two problems can be formulated as linear and quadratic programming problems, respectively (Refs. 1–2). In applications, the number of variables in each of these mathematical programming problems tends to be large. Consequently, it is important to have efficient numerical methods for their solution. The purpose of this paper is to present a method which allows the quadratic programming formulation of the elastoplastic analysis to be reformulated as an equivalent quadratic programming problem which has significantly fewer variables than the original formulation. Indeed, in Section 4, we will present details of an example for which the original quadratic programming formulation required 297 variables and for which the equivalent formulation presented here required only two variables. The method is based on a characterization of the entire family of optimal solutions for a linear programming problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935274
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