A generalized alternative theorem of partial and generalized cone subconvexlike set-valued maps and its applications in linear spaces

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. © 2012 zhi-ang zhou and jian-wen peng.