Splitting Proximal Point Algorithms for the Sum of Prox-Convex Functions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917195692376064 |
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| author | de Brito, Jose Lara, Felipe Van Thang, Tran |
| author_facet | de Brito, Jose Lara, Felipe Van Thang, Tran |
| contents | This paper addresses the minimization of a finite sum of prox-convex functions under Lipschitz continuity of each component. We propose two variants of the splitting proximal point algorithms proposed in \cite{Bacak,Bertsekas}: one deterministic with a fixed update order, and one stochastic with random sampling, and we extend them from convex to prox-convex functions. We prove global convergence for both methods under standard stepsize a\-ssump\-tions, with almost sure convergence for the stochastic variant via supermartingale theory. Numerical experiments with nonconvex quadratic functions illustrate the efficiency of the proposed methods and support the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06970 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Splitting Proximal Point Algorithms for the Sum of Prox-Convex Functions de Brito, Jose Lara, Felipe Van Thang, Tran Optimization and Control 90C26, 90C30 This paper addresses the minimization of a finite sum of prox-convex functions under Lipschitz continuity of each component. We propose two variants of the splitting proximal point algorithms proposed in \cite{Bacak,Bertsekas}: one deterministic with a fixed update order, and one stochastic with random sampling, and we extend them from convex to prox-convex functions. We prove global convergence for both methods under standard stepsize a\-ssump\-tions, with almost sure convergence for the stochastic variant via supermartingale theory. Numerical experiments with nonconvex quadratic functions illustrate the efficiency of the proposed methods and support the theoretical results. |
| title | Splitting Proximal Point Algorithms for the Sum of Prox-Convex Functions |
| topic | Optimization and Control 90C26, 90C30 |
| url | https://arxiv.org/abs/2601.06970 |