An extragradient-type algorithm for variational inequality on Hadamard manifolds

An Iterative Scheme for Generalized Equilibrium, Variational Inequality and Fixed Point Problems Based on the Extragradient Method

The problem ofgeneralized equilibrium problem is very general in the different subjects .Optimization problems, variational inequalities, Nash equilibrium problem and minimax problems are as special cases of generalized equilibrium problem. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized equilibrium problem, variational inequal...

An Inequality of Hadamard Type for Permanents

Let F be an N×N complex matrix whose jth column is the vector ~ fj in C . Let |~ fj |2 denote the sum of the absolute squares of the entries of ~ fj . Hadamard’s inequality for determinants states that | det(F )| ≤ Nj=1 |~ fj |. Here we prove a sharp upper bound on the permanent of F , which is |perm(F )| ≤ N ! NN/2 N ∏ j=1 |~ fj |, and we determine all of the cases of equality. We also discuss...

A New Version of Extragradient Method for Variational Inequality Problems

In this paper, we propose a new version of extragradient method for the variational inequality problem. The method uses a new searching direction which differs from any one in existing projection-type methods, and is of a better stepsize rule. Under a certain generalized monotonicity condition, it is proved to be globally convergent. @ 2001 Eisevier Science Ltd. All rights reserved. Keywords-Vs...

Two-Step Methods for Variational Inequalities on Hadamard Manifolds

In this paper, we suggest and analyze a two-step method for solving the variational inequalities on Hadamard manifold using the auxiliary principle technique. The convergence of this new method requires only the partially relaxed strongly monotonicity, which is a weaker condition than monotonicity. Results can be viewed as refinement and improvement of previously known results.

Explicit Iterative Method for Variational Inequalities on Hadamard Manifolds