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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.00635 |
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| _version_ | 1866917787186757632 |
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| author | Chakraborty, Abhishek Nedić, Angelia |
| author_facet | Chakraborty, Abhishek Nedić, Angelia |
| contents | We consider the mirror-prox algorithm for solving monotone Variational Inequality (VI) problems. As the mirror-prox algorithm is not practically implementable, except in special instances of VIs (such as affine VIs), we consider its implementation with Popov method updates. We provide convergence rate analysis of our proposed method for a monotone VI with a Lipschitz continuous mapping. We establish a convergence rate of $O(1/t)$, in terms of the number $t$ of iterations, for the dual gap function. Simulations on a two player matrix game corroborate our findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00635 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Popov Mirror-Prox for solving Variational Inequalities Chakraborty, Abhishek Nedić, Angelia Optimization and Control We consider the mirror-prox algorithm for solving monotone Variational Inequality (VI) problems. As the mirror-prox algorithm is not practically implementable, except in special instances of VIs (such as affine VIs), we consider its implementation with Popov method updates. We provide convergence rate analysis of our proposed method for a monotone VI with a Lipschitz continuous mapping. We establish a convergence rate of $O(1/t)$, in terms of the number $t$ of iterations, for the dual gap function. Simulations on a two player matrix game corroborate our findings. |
| title | Popov Mirror-Prox for solving Variational Inequalities |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2404.00635 |