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 theoren~ 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.

Kuhn-tucker condition and wolfe duality of preinvex set-valued optimization

“…Recently, Refs. [8,9] introduced the concept of α-order cone convex set-valued functions and defined a concept of α-order contingent derivative which makes the α-order cone convex set-valued be derivatiable.…”

“…[3]. References [4][5][6][7] applied the concept of epiderivatives to establish optimality conditions of constrained set-valued optimization. Recently, Refs.…”