{"ID":2845786,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.03442","arxiv_id":"2511.03442","title":"Proximal gradient descent on the smoothed duality gap to solve saddle point problems","abstract":"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.","short_abstract":"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,...","url_abs":"https://arxiv.org/abs/2511.03442","url_pdf":"https://arxiv.org/pdf/2511.03442v1","authors":"[\"Olivier Fercoq\"]","published":"2025-11-05T13:02:32Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}