The Strong Convergence of Prediction-Correction and Relaxed Hybrid Steepest-Descent Method for Variational Inequalities

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

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...

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...

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...

Hybrid Steepest Descent Method for Solving Hierarchical Fixed Point Approach to Variational Inequalities Constrained Optimization Problem

An explicit hierarchical fixed point algorithm is introduced to solve the monotone variational inequality over the fixed point set of a nonexpansive mapping. This paper discusses a monotone variational inequality with variational constraint and convex optimization problems over the fixed point set of a nonexpansive mapping. The strong convergence for the proposed algorithm to the solution is gu...