SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916225116798976 |
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| author | Behmandpoor, Pourya Latafat, Puya Themelis, Andreas Moonen, Marc Patrinos, Panagiotis |
| author_facet | Behmandpoor, Pourya Latafat, Puya Themelis, Andreas Moonen, Marc Patrinos, Panagiotis |
| contents | We introduce SPIRAL, a SuPerlinearly convergent Incremental pRoximal ALgorithm, for solving nonconvex regularized finite sum problems under a relative smoothness assumption. Each iteration of SPIRAL consists of an inner and an outer loop. It combines incremental gradient updates with a linesearch that has the remarkable property of never being triggered asymptotically, leading to superlinear convergence under mild assumptions at the limit point. Simulation results with L-BFGS directions on different convex, nonconvex, and non-Lipschitz differentiable problems show that our algorithm, as well as its adaptive variant, are competitive to the state of the art. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_08195 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization Behmandpoor, Pourya Latafat, Puya Themelis, Andreas Moonen, Marc Patrinos, Panagiotis Optimization and Control Machine Learning 90C06, 90C25, 90C26, 49J52, 49J53, 90C53 We introduce SPIRAL, a SuPerlinearly convergent Incremental pRoximal ALgorithm, for solving nonconvex regularized finite sum problems under a relative smoothness assumption. Each iteration of SPIRAL consists of an inner and an outer loop. It combines incremental gradient updates with a linesearch that has the remarkable property of never being triggered asymptotically, leading to superlinear convergence under mild assumptions at the limit point. Simulation results with L-BFGS directions on different convex, nonconvex, and non-Lipschitz differentiable problems show that our algorithm, as well as its adaptive variant, are competitive to the state of the art. |
| title | SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization |
| topic | Optimization and Control Machine Learning 90C06, 90C25, 90C26, 49J52, 49J53, 90C53 |
| url | https://arxiv.org/abs/2207.08195 |