On modified hybrid steepest-descent method for variational inequalities

Assume a nonlinear operator F is strongly monotone and Lipschitzian on a nonempty closed convex Subset C of a real Hilbert space H. We devise an iterative algorithm Xn+1 = alpha x(n) + (1 - alpha)Tx(n) - lambda(n+1)mu F(Tx(n)), n >= 0, which generates a sequence {x(n)} from an arbitrary initial point x(0) is an element of H. The sequence {x(n)} is shown to converge in norm to the unique solution x* of a variational inequality under some mild conditions. Application to constrained pseudoinverse is included