Variational Inequality Problem Of Unconstrained Optimization Problems

—In this paper, we study the variational inequality problem (VIP) in Banach space X and extend the results for R? in[4] by N.Yamashita and others.We also constitute an unconstrained optimization reformulation which is equivalent to V7P, so that we can use an iterative method for solving VIP. Finally, wo present a descent method for solving VIP and study a global error bound for unconstrained optimization reformulation in order to discuss the convergence of itinerative method.