Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities

Assume that F is a nonlinear operator on a real Hilbert space H which is -strongly monotone and -Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed point sets of a finite number of nonexpansive mappings on H. We devise an iterative algorithm which generates a sequence (x_n) from an arbitrary initial point x₀H. The sequence (x_n) is shown to converge in norm to the unique solution u* of the variational inequality Applications to constrained pseudoinverse are included.