Stability in Linear Optimization Under Perturbations of the Left-Hand Side Coefficients

This paper studies stability properties of linear optimization problems with finitely many variables and an arbitrary number of constraints, when only left hand side coefficients can be perturbed. The coefficients of the constraints are assumed to be continuous functions with respect to an index which ranges on certain compact Hausdorff topological space, and these properties are preserved by the admissible perturbations. More in detail, the paper analyzes the continuity properties of the feasible set, the optimal set and the optimal value, as well as the preservation of desirable properties (boundedness, uniqueness) of the feasible and of the optimal sets, under sufficiently small perturbations.

Research supported by the grants: BASAL PFB-03 (Chile), FONDECYT 1130176 (Chile) and MTM2011-29064-C03-01 (Spain). Research supported by the grant MTM2014-59179-C2-1-P (Spain) and the Discovery Projects DP120100467 and DP110102011 (Australian Research Council). Research supported by the MIUR project ’Variational and Topological Methods in the Study of Nonlinear Phenomena” (2009).