On characterization of solution sets of set-valued pseudoinvex optimization problems
The authors consider Stampaccia variational-like inequalities in terms of a normal subdifferential for set-valued maps. In Section 2, some basic definitions and preliminaries are given. Section 3 presents some relationships between Stampaccia variational-like inequalities and scalarized set-valued optimization problems. In particular, it is proven that any solution of a scalarized weak set-valued optimization problem is also a solution of the problem with Stampaccia variational-like inequalities (Theorem 3.1 and for real vector-valued functions, Theorem 3.2). In Section 4, some characterizations of the solution sets of set-valued optimization problems under the condition of pseudoinvexity are presented. The derived results hold also for the convex case which extends the results of earlier works.
scientific article; zbMATH DE number 6380436
scientific article