On Non-Monotone Variational Inequalities
Optimization and Control
2025-10-06 v1
Abstract
In this paper, we provide some sufficient conditions for the existence of solutions to non-monotone Variational Inequalities (VIs) based on inverse mapping theory and degree theory. We have obtained several applicable sufficient conditions for this problem and have introduced a sufficient condition for the existence of a Minty solution. We have shown that the Korpelevich and Popov methods converge to a solution of a non-monotone VI, provided that a Minty solution exists.
Keywords
Cite
@article{arxiv.2510.02724,
title = {On Non-Monotone Variational Inequalities},
author = {Sina Arefizadeh and Angelia Nedić},
journal= {arXiv preprint arXiv:2510.02724},
year = {2025}
}