PROXIMAL ALGORTHM FOR MONOTONE VARIATIONAL INEQUALITY PROBLEMS

Abstract

In this paper, we introduce a new proximal algorithm for monotone variational inequality problems in a general form in space Rⁿ with cost mappings are monotone, L-Lipschitz continuous on the whole space Rⁿ. The proposed algorithm involves only one proximal operator periteration and combines proximal operators with the Halpern iteration technique. The strong convergence result of the iterative sequence generated by the proposed algorithm is established, under mild conditions, in space Rⁿ.