Hybrid Steepest-Descent Methods for Solving Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators

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.

Abstract licence: CC BY

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