Mirror-Free Proximal Methods
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911534633975808 |
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| author | Vyas, Abhijeet Bullins, Brian |
| author_facet | Vyas, Abhijeet Bullins, Brian |
| contents | We present a \emph{mirror-free} mirror prox (MFMP) algorithm, which extends the classic approach of Nemirovski (2004) to allow for proximal-like updates without the explicit need for a mirror map. We further analyze the convergence of our method under suitable notions of relative smoothness and relative Lipschitzness, for which we introduce a relaxation of the standard Bregman divergence in terms of more general potential operators. Finally, we show how a strongly monotone variant of our method allows us to solve regularized Taylor-expansion subproblems that appear in both second- and third-order smooth min-max optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20918 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mirror-Free Proximal Methods Vyas, Abhijeet Bullins, Brian Optimization and Control We present a \emph{mirror-free} mirror prox (MFMP) algorithm, which extends the classic approach of Nemirovski (2004) to allow for proximal-like updates without the explicit need for a mirror map. We further analyze the convergence of our method under suitable notions of relative smoothness and relative Lipschitzness, for which we introduce a relaxation of the standard Bregman divergence in terms of more general potential operators. Finally, we show how a strongly monotone variant of our method allows us to solve regularized Taylor-expansion subproblems that appear in both second- and third-order smooth min-max optimization. |
| title | Mirror-Free Proximal Methods |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.20918 |