ITERATIVE SCHEMES FOR VARIATIONAL INEQUALITIES WITH BOUNDEDLY LIPSCHITZIAN AND STRONGLY MONOTONE MAPPINGS

In this paper, for solving a variational inequality problem governed by a boundedly Lipschitzian and strongly monotone mapping over the set of common fixed points of a sufficiently large finite family of nonexpansive mappings on Hilbert spaces, we propose a new strongly convergent self-adaptive hybrid steepest-descent block-iterative scheme.The strong convergence of any sequence, generated by this scheme, is proved under weaker conditions on iterative parameters without any additional assumption on the family of fixed point sets as well as the dimension of the spaces.An application to networked systems and a convex optimization problem over the intersection of a finite family of closed convex subsets with numerical experiments are given for illustration.