Constraint augmentation in pseudo-singularly perturbed linear programs

K Avrachenkov, R Burachik, Jerzy Filar, Vladimir Gaitsgory

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    In this paper we study a linear programming problem with a linear perturbation introduced through a parameter ε > 0. We identify and analyze an unusual asymptotic phenomenon in such a linear program. Namely, discontinuous limiting behavior of the optimal objective function value of such a linear program may occur even when the rank of the coefficient matrix of the constraints is unchanged by the perturbation. We show that, under mild conditions, this phenomenon is a result of the classical Slater constraint qualification being violated at the limit and propose an iterative, constraint augmentation approach for resolving this problem.

    Original languageEnglish
    Pages (from-to)179-208
    Number of pages30
    JournalMathematical Programming
    Volume132
    Issue number1-2
    DOIs
    Publication statusPublished - Apr 2012

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