A relaxed projection method for variational inequalities
Mathematical Programming: Series A and B
On the projected subgradient method for nonsmooth convex optimization in a Hilbert space
Mathematical Programming: Series A and B
A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces
Mathematics of Operations Research
SIAM Journal on Optimization
A Hybrid Extragradient-Viscosity Method for Monotone Operators and Fixed Point Problems
SIAM Journal on Control and Optimization
Convexly constrained linear inverse problems: iterativeleast-squares and regularization
IEEE Transactions on Signal Processing
A projected subgradient method for solving generalized mixed variational inequalities
Operations Research Letters
A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems
Journal of Global Optimization
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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.