English

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}
}
R2 v1 2026-07-01T06:14:43.829Z