A new class of projection and contraction methods for solving variational inequality problems *

This paper presents a new class of projection and contraction methods for solving monotone variational inequality problems. The methods can be viewed as combinations of some existing projection and contraction methods and the method of shortest residuals, a special case of conjugate gradient methods for solving unconstrained nonlinear programming problems. Under mild assumptions, we show the global convergence of the methods. Some preliminary computational results are reported to show the efficiency of the methods.