REGULARIZATION AND ITERATION METHODS FOR A CLASS OF MONOTONE VARIATIONAL INEQUALITIES

Abstract

We consider the monotone variational inequality of finding $x^*\in C$ such that $\langle (I-T)x^*,x-x^*\rangle \ge 0$ for $x\in C$, where $C$ is a closed convex subset of a real Hilbert space and $T$ is a nonexpansive self-mapping of $C$. Techniques of nonexpansive mappings are applied to regularize this variational inequality. The regularized solutions and an iteration process are shown to converge in norm to a solution of this variational inequality.