Multi-step hybrid steepest-descent methods for split feasibility problems with hierarchical variational inequality problem constraints

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...

Iterative algorithms based on the hybrid steepest descent method for the split feasibility problem

In this paper, we introduce two iterative algorithms based on the hybrid steepest descent method for solving the split feasibility problem. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a solution of the split feasibility problem, which is a solution of a certain variational inequality. In particular, the minimum norm solution of the spl...

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...

The Split Variational Inequality Problem

We propose a new variational problem which we call the Split Variational Inequality Problem (SVIP). It entails …nding a solution of one Variational Inequality Problem (VIP), the image of which under a given bounded linear transformation is a solution of another VIP. We construct iterative algorithms that solve such problems, under reasonable conditions, in Hilbert space and then discuss special...