On the generalized Fritz John optimality conditions of vector optimization with set-valued maps under benson proper efficiency

Abstract

A kind of tangent derivative and the concepts of strong and weak pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the setvalued map is specialized to be a single-valued map.