Éditeur(s) : HAL CCSDYokohama Résumé : International audience We introduce a convergent method for approximating a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a monotone equilibrium problem. Using the main convergence theorem we obtain results which improve, develop and unify several results in fixed point problems, variational inequalities and equilibrium problems. Journal of Nonlinear and Convex Analysis
Éditeur(s) : HAL CCSD Résumé : International audience The main purpose of this note is to propose viscosity approximation methods which amount to selecting a particular fixed-point of a given nonexpansive self mapping in a general Hilbert space. The connection with the selection principles of Attouch, in the context of convex minimization and monotone inclusion problems, is made and an application to a semi-coercive elliptic problem is then stated. Key words: nonexpansive mappings, fixed-points, monotone operators, iterative methods, convex optimization, selection, penalty ... Lecture notes in economics and mathematical systems
Éditeur(s) : HAL CCSDSpringerOpen Résumé : International audience We introduce methods which seem to be a new and promising tool in hierarchical fixed-point problems. The goal of this note is to analyze the convergence properties of these new types of approximating methods for fixed-point problems. The limit attained by these curves is the solution of the general variational inequality,, where denotes the normal cone to the set of fixed point of the original nonexpansive mapping and a suitable nonexpansive mapping criterion. The link with other approximation schemes in this field is also made. ISSN: 1687-1820
Éditeur(s) : HAL CCSDSpringer Verlag Résumé : International audience We study the convergence of the Mann Iteration applied to the partial complement of a firmly nonexpansive operator with respect to a linear subspace of a Hilbert space. A new concept considered here. A regularized version is also proposed. Furthermore, to motivate this concept, some applications to robust regression procedures and location problems are proposed. ISSN: 1862-4472
Éditeur(s) : HAL CCSDElsevier Résumé : International audience The aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed-point of a given nonexpansive self-mapping. Journal of Mathematical Analysis and applications
Éditeur(s) : HAL CCSDTaylor & Francis Résumé : International audience This article is concerned with a generalization of the hybrid steepest descent method from variational inequalities to the multivalued case. This will be reached by replacing the multivalued operator by its Yosida approximate, which is always Lipschitz continuous. It is worth mentioning that the hybrid steepest descent method is an algorithmic solution to variational inequality problems over the fixed point set of certain nonexpansive mappings and has remarkable applicability to the constrained nonlinear inverse problems like image recovery and MIMO communication systems ISSN: 0163-0563
Éditeur(s) : HAL CCSDTaylor & Francis Résumé : International audience We study the convergence of a variable version of the Krasnoselski-Mann algorithm applied to a primal dual fixed point problem. The link with Spingarn's partial inverse method is made, and an application to feasibility problems and mathematical programming is also proposed. ISSN: 0163-0563
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