Exploiting different tangent cones, many derivatives for set-valued functions have been introduced and considered to study optimality. The main goal of the paper is to address a general concept of K-epiderivative and to employ it to develop a quite general scheme for necesary optimality...

Exploiting different tangent cones, many derivatives for set-valued functions have been introduced and considered to study optimality. The main goal of the paper is to address a general concept of K-epiderivative and to employ it to develop a quite general scheme for necesary optimality...

For various classes of vector optimization problems, necessary and sufficient optimality conditions are developed in terms of first order tangent cones and second order tangent sets and cones. Additional remarks are also made.

The generalized contingent epiderivative of set-valued maps is introduced in this paper and its relationship to the contingent epiderivative is investigated. A unified necessary and sufficient optimality condition is derived in terms of the generalized contingent epiderivative. The existence of...

In this paper, we are concerned with a set-valued fractional extremal programming problem under inclusion constraints. Our approach consists of using the extremal principle (an approach initiated by Mordukhovich, which does not involve any convex approximations and convex separation arguments)...

In this paper, we propose the concept of a second-order composed contingent derivative for set-valued maps, discuss its relationship to the second-order contingent derivative and investigate some of its special properties. By virtue of the second-order composed contingent derivative, we extend...

The generalized contingent epiderivative of set-valued maps is introduced in this paper and its relationship to the contingent epiderivative is investigated. A unified necessary and sufficient optimality condition is derived in terms of the generalized contingent epiderivative. The existence of...

In this paper, we deal with the extended well-posedness and strongly extended well-posedness of set-valued optimization problems. These two concepts are generalizations of the extended well-posedness of real-valued optimization probems defined by Zolezzi. We obtain some criteria and...

A a set-valued optimization problem min C F(x), x ∈X 0 , is considered, where X 0 ⊂ X, X and Y are normed spaces, F: X 0 ⊂ Y is a set-valued function and C ⊂ Y is a closed cone. The solutions of the set-valued problem are defined as pairs (x 0 ,y 0 ), y 0 ∈F(x 0 ), and are called...