{"ID":2860786,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.02724","arxiv_id":"2510.02724","title":"On Non-Monotone Variational Inequalities","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.","short_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...","url_abs":"https://arxiv.org/abs/2510.02724","url_pdf":"https://arxiv.org/pdf/2510.02724v1","authors":"[\"Sina Arefizadeh\",\"Angelia Nedić\"]","published":"2025-10-03T04:58:34Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}