Optimality conditions without continuity in multivalued optimization using approximations as generalized derivatives

Abstract

We propose a notion of approximations as generalized derivatives for multivalued mappings and establish both necessary and sufficient conditions of orders 1 and 2 for various kinds of efficiency in multivalued vector optimization without convexity and even continuity. Compactness assumptions are also relaxed. Our theorems include several recent existing results in the literature as special cases.