Approximate efficiency in set-valued optimization with variable order

Abstract

We consider constrained set-valued optimization problems with variable order in view of two main purposes: one is to deduce conditions for stability of minima of such problems at the perturbations of the objective map and the set of constraints, and the second is to study some possibilities of recovering optimization problems with fixed order. We apply our results in order to obtain optimality conditions for such problems. The main tools we use are four types of cone enlargements.