In this paper, we consider a bilevel vector optimization problem where objective and constraints are set valued maps. Our approach consists of using a support function [1, 2, 3, 14, 15, 32] together with the convex separation principle for the study of necessary optimality conditions for D.C bilevel set valued optimization problems. We give optimality conditions in terms of the strong subdiffer...

Let C be a nonempty closed subset of the real normed linear space X. In this paper we determine the extent to which formulas for the Clarke subdifferential of the distance for C, de(x) := inf I/Y.rll, be< which are valid when C is convex, remain valid when C is not convex. The assumption of subdifferential regularity for d, plays an important role. When x 4 C, the most precise results also requ...

It is shown that a locally Lipschitz function is approximately convex if, and only if, its Clarke subdifferential is a submonotone operator. Consequently, in finite dimensions, the class of locally Lipschitz approximately convex functions coincides with the class of lower-C functions. Directional approximate convexity is introduced and shown to be a natural extension of the class of lower-C fun...

This paper is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipsch...

This paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main focus is the so-called (full and partial) second-order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of first-order...

The paper presents a semismooth inexact Newton-type method for solving optimal power flow (OPF) problem. By introducing the nonlinear complementarity problem (NCP) function, the Karush-KuhnTucker (KKT) conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by an improved inexact LevenbergMar...

The paper concerns optimal control problems for dynamic systems governed by a parametric family of discrete approximations of control systems with continuous time. Discrete approximations play an important role in both qualitative and numerical aspects of optimal control and occupy an intermediate position between discrete-time and continuous-time control systems. The central result in optimal ...

In this paper we consider evolution inclusions driven by a time dependent subdifferential operator and a set-valued perturbation term. First we show that the problem with a convex-valued, h∗-u.s.c. orientor field (i.e. perturbation term) has a nonempty solution set which is an Rδ-set in C(T,H), in particular then compact and acyclic. For the non convex problem (i.e. the orientor field is non co...

To a convex set in a Banach space we associate a convex function (the separating function), whose subdifferential provides useful information on the nature of the supporting and exposed points of the convex set. These points are shown to be also connected to the solutions of a minimization problem involving the separating function. We investigate some relevant properties of this function and of...

In this paper we introduce and study enhanced notions of relative Pareto minimizers to constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency /minimality. Using advanced tools of variational analysis and generalized differentiation, we esta...