Copyright © 2012 Zhi-Ang Zhou and Jian-Wen Peng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We first introduce a new notion of the partial and generalized cone subconvexlike set-valued map and give an equivalent characterization of the partial and generalized cone subconvexlike set-valued map in linear spaces. Secondly, a generalized alternative theorem of the partial and generalized cone subconvexlike set-valued map was presented. Finally, Kuhn-Tucker conditions of set-valued optimization problems were established in the sense of globally proper efficiency.