On Non-Monotone Variational Inequalities
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909823026593792 |
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| author | Arefizadeh, Sina Nedić, Angelia |
| author_facet | Arefizadeh, Sina Nedić, Angelia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02724 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Non-Monotone Variational Inequalities Arefizadeh, Sina Nedić, Angelia Optimization and Control 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. |
| title | On Non-Monotone Variational Inequalities |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.02724 |