Éditeur(s) : HAL CCSD Yokohama
Résumé : International audience
We make use of the viscosity technique to develop a convergent method for approximating a common element of the set of fixed points of a demicontractive operator and the set of solutions of a monotone equilibrium problem. The proposed algorithm is obtained by coupling a modified hybrid steepest descent method with the extragradient algorithm. Under mild conditions, the strong convergence of the sequences generated by the algorithm is obtained. Using this result we obtain two corollaries which improve or develop several corresponding results in this field.
Journal of Nonlinear and Convex Analysis

hal-00779988
https://hal.univ-antilles.fr/hal-00779988

Éditeur(s) : HAL CCSD Taylor & 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

hal-00776641
https://hal.univ-antilles.fr/hal-00776641
DOI : 10.1080/01630563.2011.619676