Constraint augmentation in pseudo-singularly perturbed linear programs
Date
2012
Authors
Avrachenkov, K.
Burachik, R.S.
Filar, J.A.
Gaitsgory, V.
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Journal article
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Mathematical programming, 2012; 132(1/2):179-208
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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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Copyright 2010 Springer and Mathematical Programming Society