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arXiv · 2510.02724

On Non-Monotone Variational Inequalities

Sina Arefizadeh·Angelia Nedić
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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.

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Sina Arefizadeh, Angelia Nedić. 2025-10-03. On Non-Monotone Variational Inequalities. https://arxiv.org/abs/2510.02724

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