${\cal T}$-class algorithms for pseudocontractions and $\kappa$-strict pseudocontractions in Hilbert spaces

Jean-Philippe Chancelier (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous mapping. The last problem being related to finding fixed points of pseudocontractions. These algorithms were already studied in [G.L. Acedo, H.-K. Xu] and [N. Nadezhkina, W. Takahashi] but our aim here is to provide the links between these know algorithms and the general framework of ${\cal T}$-class algorithms studied in [H.H. Bauschke, P.L. Combettes].

Mots clés: Fejer Monotone; Nonexpansive mappings; Fixed point; Fejer Monotone.

Domaines: Optimisation et contrôle [math.OC]

Jean-Philippe Chancelier. ${\cal T}$-class algorithms for pseudocontractions and $\kappa$-strict pseudocontractions in Hilbert spaces. 2007. ⟨hal-00193621⟩