Estimating Sequences with Memory for Minimizing Convex Non-smooth Composite Functions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911190823731200 |
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| author | Dosti, Endrit Vorobyov, Sergiy A. Charalambous, Themistoklis |
| author_facet | Dosti, Endrit Vorobyov, Sergiy A. Charalambous, Themistoklis |
| contents | First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce a new class of generalized composite estimating sequences, devised by exploiting the information embedded in the iterates generated during the minimization process. Building on these sequences, we propose a novel accelerated first-order method tailored for such objective structures. This method features a backtracking line-search strategy and achieves an accelerated convergence rate, regardless of whether the true Lipschitz constant is known. Additionally, it exhibits robustness to imperfect knowledge of the strong convexity parameter, a property of significant practical importance. The method's efficiency and robustness are substantiated by comprehensive numerical evaluations on both synthetic and real-world datasets, demonstrating its effectiveness in data processing applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimating Sequences with Memory for Minimizing Convex Non-smooth Composite Functions Dosti, Endrit Vorobyov, Sergiy A. Charalambous, Themistoklis Optimization and Control First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce a new class of generalized composite estimating sequences, devised by exploiting the information embedded in the iterates generated during the minimization process. Building on these sequences, we propose a novel accelerated first-order method tailored for such objective structures. This method features a backtracking line-search strategy and achieves an accelerated convergence rate, regardless of whether the true Lipschitz constant is known. Additionally, it exhibits robustness to imperfect knowledge of the strong convexity parameter, a property of significant practical importance. The method's efficiency and robustness are substantiated by comprehensive numerical evaluations on both synthetic and real-world datasets, demonstrating its effectiveness in data processing applications. |
| title | Estimating Sequences with Memory for Minimizing Convex Non-smooth Composite Functions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.02965 |