Abstract
Arbitrary perturbations of arbitrary coefficients in linear programming models on the canonical form are studied. Perturbations that preserve stability (lower semi-continuity of the feasible set mapping) are characterized in terms of subsets of the index set of the decision variable. A necessary condition for stability is used to formulate a method for identification of unstable perturbations. Instability is illustrated in various situations including multi-level decision making, descriptions of locally and globally optimal parameters in linear parametric programming, and a marginal value formula for models with a convex objective and linear canonical constraints.
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Zlobec, S. Stability in Linear Programming Models: An Index Set Approach. Annals of Operations Research 101, 363–382 (2001). https://doi.org/10.1023/A:1010917903065
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DOI: https://doi.org/10.1023/A:1010917903065