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 ...

Cédric Bonnafé (co-directeur) Chargé de Recherche à l’Université de Franche-Comté Michel Brion Directeur de Recherche à l’Université de Grenoble 1 Michel Broué Professeur à l’Université Paris 7 Bernard Leclerc Professeur à l’Université de Caen Jean Michel Directeur de Recherche à l’Université Paris 7 Raphaël Rouquier (co-directeur) Directeur de Recherche à l’Université Paris 7 Professeur à l’Un...

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...

in this paper, we deal with the subdierential concept onhadamard spaces. flat hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in hadamard spaces is nonempty. proximal subdierentialin hadamard spaces is addressed and some basic properties are high-lighted. finally, a density theorem for subdierential set is establi...

We study eggs in PG(4n−1, q). A new model for eggs is presented in which all known examples are given. We calculate the general form of the dual egg for eggs arising from a semifield flock. Applying this to the egg obtained in L. Bader, G. Lunardon and I. Pinneri [1] from the Penttila-Williams ovoid [11], we obtain the dual egg, which is not isomorphic to any of the previous known examples, see...