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Constraint augmentation in pseudo-singularly perturbed linear programs

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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.

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Authors and Affiliations

  1. INRIA, 2004 route des lucioles-BP 93, 06902, Sophia Antipolis Cedex, France

    K. Avrachenkov

  2. Centre for Industrial and Applied Mathematics, School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA, 5095, Australia

    R. S. Burachik, J. A. Filar & V. Gaitsgory

Authors
  1. K. Avrachenkov
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  2. R. S. Burachik
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  3. J. A. Filar
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  4. V. Gaitsgory
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Corresponding author

Correspondence to V. Gaitsgory.

Additional information

The work on this project was supported by the ARC Linkage International Grants LX0560049 and LX0881972 and partially by ARC Discovery Grants DP0664330 and DP0666632.

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Avrachenkov, K., Burachik, R.S., Filar, J.A. et al. Constraint augmentation in pseudo-singularly perturbed linear programs. Math. Program. 132, 179–208 (2012). https://doi.org/10.1007/s10107-010-0388-0

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  • DOI: https://doi.org/10.1007/s10107-010-0388-0

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