Abstract:
Set-valued mappings theory and set topology theory play an important role in the stability study of set-valued optimization. In this paper, we use these theories to study the connectedness of strong efficient solution set for set-valued constrained optimization problems in locally convex spaces. Firstly, we give a conclusion of the scalarization of base functions, and discuss some properties of cone-arcwise connected set-valued mapping. Then, we give a lemma of the connectedness of strong efficient point set for set-valued constrained optimization problems when the feasible region is an arcwise connected and compact subset. At last, using this lemma, we study the connectedness of strong efficient solution set with constraints and obtain a theorem of the connectedness of strong efficient solution set with constraints. The convex sets are arc-wise connected sets and the converse is not true in general, so this study broadens the restrictions of the feasible region in some degree.