(Adaptive) Scaled gradient methods beyond locally Holder smoothness: Lyapunov analysis, convergence rate and complexity
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918200812240896 |
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| author | Ghaderi, Susan Rahimi, Morteza Moreau, Yves Ahookhosh, Masoud |
| author_facet | Ghaderi, Susan Rahimi, Morteza Moreau, Yves Ahookhosh, Masoud |
| contents | This paper addresses the unconstrained minimization of smooth convex functions whose gradients are locally Holder continuous. Building on these results, we analyze the Scaled Gradient Algorithm (SGA) under local smoothness assumptions, proving its global convergence and iteration complexity. Furthermore, under local strong convexity and the Kurdyka-Lojasiewicz (KL) inequality, we establish linear convergence rates and provide explicit complexity bounds. In particular, we show that when the gradient is locally Lipschitz continuous, SGA attains linear convergence for any KL exponent. We then introduce and analyze an adaptive variant of SGA (AdaSGA), which automatically adjusts the scaling and step-size parameters. For this method, we show global convergence, and derive local linear rates under strong convexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | (Adaptive) Scaled gradient methods beyond locally Holder smoothness: Lyapunov analysis, convergence rate and complexity Ghaderi, Susan Rahimi, Morteza Moreau, Yves Ahookhosh, Masoud Optimization and Control 90C06, 90C25, 90C26, 49J52, 49J53 This paper addresses the unconstrained minimization of smooth convex functions whose gradients are locally Holder continuous. Building on these results, we analyze the Scaled Gradient Algorithm (SGA) under local smoothness assumptions, proving its global convergence and iteration complexity. Furthermore, under local strong convexity and the Kurdyka-Lojasiewicz (KL) inequality, we establish linear convergence rates and provide explicit complexity bounds. In particular, we show that when the gradient is locally Lipschitz continuous, SGA attains linear convergence for any KL exponent. We then introduce and analyze an adaptive variant of SGA (AdaSGA), which automatically adjusts the scaling and step-size parameters. For this method, we show global convergence, and derive local linear rates under strong convexity. |
| title | (Adaptive) Scaled gradient methods beyond locally Holder smoothness: Lyapunov analysis, convergence rate and complexity |
| topic | Optimization and Control 90C06, 90C25, 90C26, 49J52, 49J53 |
| url | https://arxiv.org/abs/2511.10425 |