A a set-valued optimization problem min<Subscript> C </Subscript> F(x), x ∈X <Subscript>0</Subscript>, is considered, where X <Subscript>0</Subscript> ⊂ X, X and Y are normed spaces, F: X <Subscript>0</Subscript> ⊂ 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 <Superscript>0</Superscript>,y <Superscript>0</Superscript>), y <Superscript>0</Superscript> ∈F(x <Superscript>0</Superscript>), and are called...</superscript></superscript></superscript></superscript></subscript></subscript></subscript></subscript>

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...

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional...

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional...

This paper studies a general vector optimization problem which encompasses those related to efficiency, weak efficiency, strict efficiency, proper efficiency and approximate efficiency among others involving non necessarily preordering relations. Based on existing results about complete...

In this paper a notion of arcwise connected convex set valued mapping is introduced. Optimality conditions involving this type of data are studied.

In this paper we consider the vector optimization problem minC f(x), g(x) 2 -K, where f : Rn ! Rm and g : Rn Rp are C0,1 functions and C Rm and K Rp are closed convex cones. We give several notions of solutions (efficiency concepts), among them the notion of a properly efficient point...