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

Phan Vuong (), Jean Strodiot () and Nguyen Van ()

Journal of Global Optimization, 2014, vol. 59, issue 1, 173-190

Abstract: 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. Copyright Springer Science+Business Media New York 2014

Keywords: Variational inequality; Equilibrium problem; Viscosity approximation; Projected subgradient method; Strong convergence (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-013-0084-8

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