CONTINUITY OF APPROXIMATE WEAK EFFICIENT SOLUTION SET MAP IN PARAMETRIC SET OPTIMIZATION

The main aim of this paper is to establish the continuity of approximate weak efficient solution set map of parametric set optimization problems. Certain continuity and compactness assumptions are used to establish the upper semicontinuity of approximate weak efficient solution set map. However, an additional assumption of strict quasiconvexity of the objective map is required to establish the lower semicontinuity of approximate weak efficient solution set map. As a consequence, we also obtain the continuity of efficient and weak efficient solution set maps.