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 present new concepts of efficiency for uncertain multi-objective optimization problems. We analyze the connection between the concept of minmax robust efficiency presented by Ehrgott et al. (Eur J Oper Res, <CitationRef CitationID="CR14">2014</CitationRef>, doi:<ExternalRef> <RefSource>10.1016/j.ejor.2014.03.013</RefSource> <RefTarget Address="10.1016/j.ejor.2014.03.013" TargetType="DOI"/> </ExternalRef>) and the upper set less order...</refsource></externalref></citationref>

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>

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...

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...

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points...

We consider the classical Markowitz portfolio optimization problem with additional constraints representing so-called short sales.  The two objectives of this multiobjective problem are the expected return and the variance of a portfolio combined by a number of risky securities. A...

Local optimality conditions are given for a quadratic programming formulation of the multiset graph partitioning problem. These conditions are related to the structure of the graph and properties of the weights. Copyright Springer-Verlag Berlin Heidelberg 2002

The notion of radial epiderivative is introduced and then a necessary and sufficient condition for a point to be a weak minimal solution (weak-efficient solution) for a non-convex set-valued optimization problem is derived. Such a condition subsumes various necessary and/or sufficient conditions...

A multiobjective programming problem characterized by convex goal functions and linear inequality constraints is studied. The investigation aims to the construction of a multiobjective dual problem permitting the verification of strong duality as well as optimality conditions.  For the...