Optimality conditions for a multiobjective bilevel optimization problem involving set valued constraints

Abstract

ABSTRACT In this paper, we investigate a multiobjectif bilevel programming problem with set valued constraints in both the upper problem and the lower problem. Using the notion of the support function to the feasible set mapping, together with an appropriate constraint qualification, we establish necessary optimality conditions in terms of asymptotical pointwise compact approximations; continuity of data functions and compactness of approximations are not necessarily required. In order to get sufficient optimality conditions, we introduce generalized pseudo-invexity and quasi-invexity notions in terms of asymptotical pointwise compact approximations. Examples that illustrate our results are given.