Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities withk-Strict Pseudocontractions

Finite-Step Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities

Mann-type Steepest-descent and Modified Hybrid Steepest-descent Methods for Variational Inequalities in Banach Spaces

1Department of Mathematics, Shanghai Normal University, Shanghai; and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China 2Department of Mathematics & Statistics, College of Science, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia; and Department of Mathematics, Aligarh Muslim University, Aligarh, India 3Department of Applied Mathematics, National S...

An Application of Hybrid Steepest Descent Methods for Equilibrium Problems and Strict Pseudocontractions in Hilbert Spaces

Strong Weak Convergence Theorems of Implicit 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 with constants η > 0 and κ > 0, respectively 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 develop an implicit hybrid steepest-descent method which generates an iterative seq...

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 pseudoco...