Hybrid Steepest-Descent Methods for Solving Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators. (24th January 2010) - He, Songnian; Liang, Xiao-Lan
Abstract : LetH be a real Hilbert space and letF : H → H be a boundedly Lipschitzian and strongly monotone operator. We design three hybrid steepest descent algorithms for solving variational inequalityV I ( C, F ) of finding a pointx ∗ ∈ C such that〈 F x ∗, x − x ∗ 〉 ≥ 0, for allx ∈ C, whereC 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.