Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces

Phan Tu Vuong, Jean-Jacques Strodiot, Van Hien Nguyen

    Résultats de recherche: Contribution à un journal/une revueArticleRevue par des pairs

    Résumé

    In this paper, we introduce and study some low computational cost numerical methods for finding a solution of a variational inequality problem over the solution set of an equilibrium problem in a real Hilbert space. The strong convergence of the iterative sequences generated by the proposed algorithms is obtained by combining viscosity-type approximations with projected subgradient techniques. First a general scheme is proposed, and afterwards two practical realizations of it are studied depending on the characteristics of the feasible set. When this set is described by convex inequalities, the projections onto the feasible set are replaced by projections onto half-spaces with the consequence that most iterates are outside the feasible domain. On the other hand, when the projections onto the feasible set can be easily computed, the method generates feasible points and can be considered as a generalization of Maingé's method to equilibrium problem constraints. In both cases, the strong convergence of the sequences generated by the proposed algorithms is proven.

    langue originaleAnglais
    Pages (de - à)1-18
    Nombre de pages18
    journalJournal of Global Optimization
    Les DOIs
    Etat de la publicationAccepté/sous presse - 19 juin 2013

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