Proximal gradient descent on the smoothed duality gap to solve saddle point problems
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918187295047680 |
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| author | Fercoq, Olivier |
| author_facet | Fercoq, Olivier |
| contents | In this paper, we minimize the self-centered smoothed gap, a recently introduced optimality measure, in order to solve convex-concave saddle point problems. The self-centered smoothed gap can be computed as the sum of a convex, possibly nonsmooth function and a smooth weakly convex function. Although it is not convex, we propose an algorithm that minimizes this quantity, effectively reducing convex-concave saddle point problems to a minimization problem. Its worst case complexity is comparable to the one of the restarted and averaged primal dual hybrid gradient method, and the algorithm enjoys linear convergence in favorable cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proximal gradient descent on the smoothed duality gap to solve saddle point problems Fercoq, Olivier Optimization and Control In this paper, we minimize the self-centered smoothed gap, a recently introduced optimality measure, in order to solve convex-concave saddle point problems. The self-centered smoothed gap can be computed as the sum of a convex, possibly nonsmooth function and a smooth weakly convex function. Although it is not convex, we propose an algorithm that minimizes this quantity, effectively reducing convex-concave saddle point problems to a minimization problem. Its worst case complexity is comparable to the one of the restarted and averaged primal dual hybrid gradient method, and the algorithm enjoys linear convergence in favorable cases. |
| title | Proximal gradient descent on the smoothed duality gap to solve saddle point problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.03442 |