In this paper, such new definitions as D-B-preinvexity, strictly D-B-preinvexity and explicitly D-B-preinvexity for vector-valued mappings are firstly introduced. Then, a sufficient condition of D-B-preinvex mappings is shown. And then the relationship between the explicitly D-B-preinvcxity and the strictly D-B-preinvexity is discussed. Finally, some properties of D-B-preinvex type mappings are given.
In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subdifferential characterizations of optimal value functions are given. Using these properties,we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.
WANG Changyu, YANG Xiaoqi & YANG Xinmin Institute oi Operations Research, Qufu Normal University, Qufu 273165, China
