extragradient method – Optimization Online

An extragradient method for solving variational inequalities without monotonicity

Published: 2019/01/29, Updated: 2019/03/30

Complementarity and Variational Inequalities extragradient method, global convergence, projection methods, quasimonotone, variational inequality

A new extragradient projection method is devised in this paper, which does not obviously require generalized monotonicity and assumes only that the so-called dual variational inequality has a solution in order to ensure its global convergence. In particular, it applies to quasimonotone variational inequality having a nontrivial solution. ArticleDownload View PDF

Projected Reflected Gradient Methods for Monotone Variational Inequalities

Published: 2015/03/20

Yura Malitsky

Complementarity and Variational Inequalities extragradient method, monotone mapping, projection methods, variational inequality

This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a constant stepsize. It is similar to the projected gradient method, namely, the method requires only one projection onto the feasible set and only … Read more