The hybrid steepest descent method for solving variational inequality over triple hierarchical problems

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 Free Line Search Steepest Descent Method for Solving Unconstrained Optimization Problems

In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...

Steepest descent method for solving zero-one nonlinear programming problems

In this paper we use steepest descent method for solving zero-one nonlinear programming problem. Using penalty function we transform this problem to an unconstrained optimization problem and then by steepest descent method we obtain the original problem optimal solution. 2007 Elsevier Inc. All rights reserved.

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...

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