LAGRANGE MULTIPLIER RULE FOR NONCONVEX SET-VALUED OPTIMIZATION PROBLEM

In this paper, in terms of circatangent epiderivative, a new kind of weak subdifferential for set-valued mappings is introduced. An existence theorem of this kind of weak subgradient is established. In terms of Lagrange multiplier, necessary and sufficient optimality conditions are established for set-valued optimization problems with constraint sets being determined by a geometric set and a cone-convex set-valued mapping. In particular, the necessary optimality conditions do not require any convexity of the objective mapping and the geometric set.