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Asymptotic Linear Programming

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  • Robert G. Jeroslow

    (Carnegie-Mellon University, Pittsburgh, Pennsylvania)

Abstract

This paper studies the linear programming problem in which all coefficients (even those of the stipulations matrix) are rational functions of a single parameter t called “time,” and provides an algorithm that can solve problems of the following two types: (1) Steady-state behavior [the algorithm can be used to determine the functional form x ( t ) of the optimal solution as a function of t , this form being valid for all “sufficiently large” values of t ], and (2) sensitivity analysis [if a value t 0 of “time” is given, the algorithm can be used to determine the two possible functional forms of the optimal solution for all values of t “sufficiently close” to t 0 (the first functional form valid for t t 0 , the second for t t 0 )]. In addition, the paper gives certain qualitative information regarding steady-state behavior, including the following result: If for some one of the properties of consistency, boundedness, or bounded constraint set, there exists a sequence t n ↗ +∞ such that the linear program at n has this property for all n , then the program has this property for all “sufficiently large” values of t .

Suggested Citation

  • Robert G. Jeroslow, 1973. "Asymptotic Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1128-1141, October.
    • Handle: RePEc:inm:oropre:v:21:y:1973:i:5:p:1128-1141
    DOI: 10.1287/opre.21.5.1128
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    Cited by:

    1. Vladimir Ejov & Jerzy Filar, 2006. "Gröbner bases in Asymptotic Analysis of Perturbed Polynomial Programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 1-16, August.
    2. Michael O’Sullivan & Arthur F. Veinott, Jr., 2017. "Polynomial-Time Computation of Strong and n -Present-Value Optimal Policies in Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 577-598, August.

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