Stability in disjunctive optimization II:continuity of the feasible and optimal set

Abstract

A disjunctive linear optimization problem is to minimize a function over a feasible set which is the union of (perhaps infinitely many) convex sets. The classofdisjunctiveoptimization problems contains many classes of optimization problems which look at the first sight very different from their structure (f.e. semi-infinite and mixed-integer linear optimization problems, certain non-linear approximation problems, fractional pro¬gramming, linear complementary problems). Our purpose in this paper is to investigate the disjunctive linear optimization problem in dependence on the involved mappings. Especially, we establish necessary and sufficient conditions for the upper and lower semicontinuity of the feasible and optimal set mapping. Examples will illustrate the difficulties and characteristics to derive such conditions in parametric disjunctive programming