## 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 language | English |
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Pages (from-to) | 179-208 |

Number of pages | 30 |

Journal | Mathematical Programming |

Volume | 132 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Apr 2012 |