A smoothing homotopy method for solving variational inequalities

Abstract: In this paper, a new homotopy method for solving the variational inequality problem : find such that , for all , where is a nonempty closed convex subset of and is a continuously differentiable mapping, is proposed. The homotopy equation is constructed based on the smooth approximation to Robinson’s normal equation of variational inequality problem, where the smooth approximation function of the projection function is an arbitrary one such that for any and , . Under a weak condition on the defining mapping , which is needed for the existence of a solution to , for the starting point chosen almost everywhere in , existence and convergence of a smooth homotopy pathway to a solution of are proved. Several numerical experiments indicate that the method is efficient. [Copyright &y& Elsevier]