María Josefa Cánovas and Juan Parra (Operations Research Center, University Miguel Hernández of Elche)
Abstract: The present paper deals with uncertain linear optimization problems where the objective function coefficient vector belongs to a compact convex uncertainty set and the feasible set is described by a linear semi-infinite inequality system (finitely many variables and possibly infinitely many constrainsts), whose coefficients are also uncertain. Perturbations of both, the objective coefficient vector set and the constraint coefficient set, are measured by the Hausdorff metric. The paper is mainly concerned with analyzing the Lipschitz continuity of the optimal value function, as well as the lower and upper semicontinuity in the sense of Berge of the optimal set mapping. Inspired by Sion’s minimax theorem, a new concept of weak optimal solution set is introduced and analyzed.