Some New Characterizations Of Strictly Efficient Element For Set-valued Optimization Problems

In this paper we consider saddle points problems on ε- strictly efficient element of binary set-valued functions in Hausdorff locally convex linear topological space. Under the hypothesis of nearly conε-subconvexlike(nearly conε-Subconcavelike), by applying separation theorem for convex sets, necessary conditions of loose saddle points on ε- Strictly efficient element of binary set-valued functions are derived. In particular, the sufficient conditions and necessary conditions of loose saddle points on strictly efficient element of binary set-valued functions are also established whene=0.The strict efficiency of set-valued optimization was considered in real normed linear space by a new second-order asymptotic epiderivative. With the help of second-order asymptotic tangent cone, a new second-order asymptotic epiderivative is introduced. At the same time, an example was given to show that its existence condition is weaker than that of second-order asymptotic tangent derivative. By applying the derivative and properties of a dilating cone, an optimality necessary conditions of locally strictly efficient element for set-valued optimization was established.