On the Convergence of Proximal Algorithms for Weakly-convex Min-max Optimization
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914431690080256 |
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| author | Tapia-Riera, Guido Castera, Camille Papadakis, Nicolas |
| author_facet | Tapia-Riera, Guido Castera, Camille Papadakis, Nicolas |
| contents | We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially simplified proof compared to previous ones. It allows us to enlarge the set of admissible step-sizes. Building on this general reformulation, we also prove the convergence of a doubly proximal algorithm in the weakly convex-strongly concave setting. Finally, we show how this new result opens the way to new applications of min-max optimization algorithms for solving regularized imaging inverse problems with neural networks in a plug-and-play manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28484 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Convergence of Proximal Algorithms for Weakly-convex Min-max Optimization Tapia-Riera, Guido Castera, Camille Papadakis, Nicolas Optimization and Control We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially simplified proof compared to previous ones. It allows us to enlarge the set of admissible step-sizes. Building on this general reformulation, we also prove the convergence of a doubly proximal algorithm in the weakly convex-strongly concave setting. Finally, we show how this new result opens the way to new applications of min-max optimization algorithms for solving regularized imaging inverse problems with neural networks in a plug-and-play manner. |
| title | On the Convergence of Proximal Algorithms for Weakly-convex Min-max Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.28484 |