Résumé
In this paper, new numerical algorithms are introduced for finding the solution of a variational inequality problem whose constraint set is the common elements of the set of fixed points of a demicontractive mapping and the set of solutions of an equilibrium problem for a monotone mapping in a real Hilbert space. The strong convergence of the iterates generated by these algorithms is obtained by combining a viscosity approximation method with an extragradient method. First, this is done when the basic iteration comes directly from the extragradient method, under a Lipschitz-type condition on the equilibrium function. Then, it is shown that this rather strong condition can be omitted when an Armijo-backtracking linesearch is incorporated into the extragradient iteration. The particular case of variational inequality problems is also examined.
langue originale | Anglais |
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Pages (de - à) | 429-451 |
Nombre de pages | 23 |
journal | Optimization |
Volume | 64 |
Numéro de publication | 2 |
Les DOIs | |
Etat de la publication | Publié - 1 janv. 2015 |