Randomized coordinate gradient descent almost surely escapes strict saddle points
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866913983304302592 |
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| author | Chen, Ziang Li, Yingzhou Li, Zihao |
| author_facet | Chen, Ziang Li, Yingzhou Li, Zihao |
| contents | We analyze the behavior of randomized coordinate gradient descent for nonconvex optimization, proving that under standard assumptions, the iterates almost surely escape strict saddle points. By formulating the method as a nonlinear random dynamical system and characterizing neighborhoods of critical points, we establish this result through the center-stable manifold theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Randomized coordinate gradient descent almost surely escapes strict saddle points Chen, Ziang Li, Yingzhou Li, Zihao Optimization and Control Numerical Analysis Dynamical Systems Probability We analyze the behavior of randomized coordinate gradient descent for nonconvex optimization, proving that under standard assumptions, the iterates almost surely escape strict saddle points. By formulating the method as a nonlinear random dynamical system and characterizing neighborhoods of critical points, we establish this result through the center-stable manifold theorem. |
| title | Randomized coordinate gradient descent almost surely escapes strict saddle points |
| topic | Optimization and Control Numerical Analysis Dynamical Systems Probability |
| url | https://arxiv.org/abs/2508.07535 |