An Explicit Parallel Algorithm for Variational Inequalities

The paper proposes an explicit parallel iterative algorithm for solving variational inequalities over the intersection of fixed point sets of finitely many demicontractive mappings. The algorithm combines the steepest descent method with the Krasnosel’skii–Mann type method and the splitting-up technique. The strongly convergent theorem is established under fewer restrictions imposed on parameters and mappings. Several applications of the algorithm to other problems are presented. We also illustrate the convergence of the algorithm and compare it with others by considering some preliminary numerical experiments.