Relaxed extragradient methods for systems of variational inequalities.

In this paper, we introduce a relaxed extragradient iterative algorithm for finding a common element of the set of solutions of a general mixed equilibrium problem, the set of solutions of general system of variational inequalities, the set of solutions of finitely many variational inclusions, and the set of common fixed points of finitely many nonexpansive mappings and a strict pseudocontraction in a real Hilbert space. The iterative algorithm is based on Korpelevich's extragradient method, the viscosity approximation method, Mann's iterative method, and the strongly positive bounded linear operator approach. We derive the strong convergence of the iterative algorithm to a common element of these sets, which also solves some hierarchical minimization. [ABSTRACT FROM AUTHOR]