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 CCSDSpringer Verlag Résumé : International audience Based on the very recent work by Censor-Gibali-Reich (http://arxiv.org/abs/1009.3780), we propose an extension of their new variational problem (Split Variational Inequality Problem) to monotone variational inclusions. Relying on the Krasnosel'skii-Mann Theorem for averaged operators, we analyze an algorithm for solving new split monotone inclusions under weaker conditions. Our weak convergence results improve and develop previously discussed Split Variational Inequality Problems, feasibility problems and related problems and algorithms. ISSN: 0022-3239
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 Based on the very recent work by Censor and Segal (2009), and inspired by Xu (2006), Zhao and Yang (2005) , and Bauschke and Combettes (2001), we introduce and analyze an algorithm for solving the split common fixed-point problem for the wide class of quasi-nonexpansive operators in Hilbert spaces. Our results improve and develop previously discussed feasibility problems and related algorithms. ISSN: 0362-546X
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
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