Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 673932, 16 pages
doi:10.1155/2010/673932

Hybrid steepest-descent methods for solving variational inequalities governed by boundedly Lipschitzian and strongly monotone operators

Abstract

Let H be a real Hilbert space and let F:H→H be a boundedly Lipschitzian and strongly monotone operator. We design three hybrid steepest descent algorithms for solving variational inequality VI(C,F) of finding a point x∗∈C such that 〈Fx∗,x−x∗〉≥0, for all x∈C, where C is the set of fixed points of a strict pseudocontraction, or the set of common fixed points of finite strict pseudocontractions. Strong convergence of the algorithms is proved.