Characterizing the nonemptiness and compactness of weakly efficient solution sets for non-convex multiobjective optimization problems

In this paper, we demonstrate that non-convex multiobjective optimization problems have nonempty and compact weakly efficient solution sets if and only if finite scalar optimization problems have nonempty and compact solution sets under mild conditions, which partially reduces the gap between non-convex and convex multiobjective problems in characterizing the nonemptiness and compactness of weakly efficient solution sets. Two examples are provided to support the findings.