A Proximal-Gradient Method for Solving Regularized Optimization Problems with General Constraints
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908768478953472 |
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| author | Curtis, Frank E. Qu, Xiaoyi Robinson, Daniel P. |
| author_facet | Curtis, Frank E. Qu, Xiaoyi Robinson, Daniel P. |
| contents | We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step acceptance or rejection. Under various assumptions, we establish a worst-case iteration complexity result, prove that limit points are first-order KKT points, and show that manifold identification and active-set identification properties hold. Preliminary numerical experiments on a subset of the CUTEst test problems and sparse canonical correlation analysis problems demonstrate the promising performance of our approach. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Proximal-Gradient Method for Solving Regularized Optimization Problems with General Constraints Curtis, Frank E. Qu, Xiaoyi Robinson, Daniel P. Optimization and Control 49M37, 65K05, 65K10, 65Y20, 68Q25, 90C30, 90C60 We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step acceptance or rejection. Under various assumptions, we establish a worst-case iteration complexity result, prove that limit points are first-order KKT points, and show that manifold identification and active-set identification properties hold. Preliminary numerical experiments on a subset of the CUTEst test problems and sparse canonical correlation analysis problems demonstrate the promising performance of our approach. |
| title | A Proximal-Gradient Method for Solving Regularized Optimization Problems with General Constraints |
| topic | Optimization and Control 49M37, 65K05, 65K10, 65Y20, 68Q25, 90C30, 90C60 |
| url | https://arxiv.org/abs/2512.23166 |