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 = αxn + (1 − α)T xn − λn+1µF(T xn), n ≥ 0, which generates a sequence {xn} from an arbitrary initial point x0 ∈ H. The sequence {xn} 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