Regina Sandra Burachik

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Given a point-to-set operator T, we introduce the operator T " deened as T " (x) = fu : hu ? v; x ? yi 0 for all y 2 R n ; v 2 T(y)g. When T is maximal monotone T " inherits most properties of the "-subdiierential, e.g. it is bounded on bounded sets, T " (x) contains the image through T of a suuciently small ball around x, etc. We prove these and other(More)
Recently, the authors studied the connection between each maximal monotone operator T and a family H(T) of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities. The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular(More)
In this paper, we propose a new decomposition method for solving convex programming problems with separable structure. The proposed method is based on the decomposition method proposed by Chen and Teboulle and the nonlinear proximal point algorithm using Bregman function. An advantage of the proposed method is that, by a suitable choice of Bregman function,(More)
We study two outer approximation schemes, applied to the vari-ational inequality problem in reflexive Banach spaces. First we pro-1 pose a generic outer approximation scheme, and its convergence analysis unifies a wide class of outer approximation methods applied to the constrained optimization problem. As is standard in this setting, boundedness and(More)
We propose a new kind of inexact scheme for a family of generalized proximal point methods for the monotone complementarity problem. These methods, studied by Auslender, Teboulle and Ben-Tiba, converge under the sole assumption of existence of solutions. We prove convergence of our new scheme, as well as discuss its implementability. Key Words. maximal(More)
Outline 1 Abstract convexity: basic tools Outline 1 Abstract convexity: basic tools 2 Abstract Lagrangians Outline 1 Abstract convexity: basic tools 2 Abstract Lagrangians 3 Duality Scheme Outline 1 Abstract convexity: basic tools 2 Abstract Lagrangians 3 Duality Scheme 4 Strong Duality Outline 1 Abstract convexity: basic tools 2 Abstract Lagrangians 3(More)
Several finite procedures for determining the step size of the steepest descent method for uncon-strained optimization, without performing exact onedimensional minimizations, have been considered in the literature. The convergence analysis of these methods requires that the objective function have bounded level sets and that its gradient satisfy a Lipschitz(More)