Random and cyclic projection algorithms for variational inequalities

Abstract

ABSTRACT In this paper, we propose a new incremental constraint projection method (containing random projection method and cyclic projection method) for solving variational inequality problems in , where the underlying function is Lipschitz continuous and monotone plus. We focus on special structures that lend themselves to sampling, such as when X is the intersection of a large number of sets, and/or F is an expected value or is the sum of a large number of component functions. Our method requires only two projections onto a suitable halfspace which replaces the projections onto constrained set . We prove the sequence generated by our method is globally convergent to a solution of the variational inequalities in almost sure sense both random projection method and cyclic projection method. Finally, we provide numerical experiments to show the efficiency and advantage of the proposed algorithms.