Hybrid Steepest Descent Method with Variable Parameters for General Variational Inequalities

Hybrid Steepest Descent Method with Variable Parameters for General Variational Inequalities

Let H be a real Hilbert space and let C be a nonempty closed convex subset of H . Let F :H →H be an operator such that for some constants k,η > 0, F is k-Lipschitzian and η-strongly monotone on C; that is, F satisfies the following inequalities: ‖Fx− Fy‖ ≤ k‖x− y‖ and 〈Fx− Fy,x− y〉 ≥ η‖x− y‖2 for all x, y ∈ C, respectively. Recall that T is nonexpansive if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈H . We ...

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...

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...

A Generalized Hybrid Steepest-Descent Method for Variational Inequalities in Banach Spaces

The hybrid steepest-descent method introduced by Yamada 2001 is an algorithmic solution to the variational inequality problem over the fixed point set of nonlinear mapping and applicable to a broad range of convexly constrained nonlinear inverse problems in real Hilbert spaces. Lehdili and Moudafi 1996 introduced the new prox-Tikhonov regularization method for proximal point algorithm to genera...