On the solution continuity of parametric set optimization problems

The aim of this paper is to investigate the continuity of the solution set maps of set-valued vector optimization problems with set optimization criterion. First, we introduce a new concept, which is called a u-lower level map. Then, we give some sufficient conditions for the upper and lower semicontinuities of the generalized lower level map. Finally, by virtue of the semicontinuity of the u-lower level map, we obtain the continuity of the minimal solution set map to parametric set-valued vector optimization problems with set optimization criterion.