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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.16517 |
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| _version_ | 1866917480395440128 |
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| author | Mourrat, Jean-Christophe |
| author_facet | Mourrat, Jean-Christophe |
| contents | We give an example of a function satisfying a two-sided Polyak-Lojasiewicz condition but for which a gradient descent-ascent flow line fails to converge to the saddle point, circling around it instead. We can even impose the function to be strongly convex in one variable and to satisfy a PL condition in the other variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16517 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PL conditions do not guarantee convergence of gradient descent-ascent dynamics Mourrat, Jean-Christophe Optimization and Control 90C47, 49J35 We give an example of a function satisfying a two-sided Polyak-Lojasiewicz condition but for which a gradient descent-ascent flow line fails to converge to the saddle point, circling around it instead. We can even impose the function to be strongly convex in one variable and to satisfy a PL condition in the other variable. |
| title | PL conditions do not guarantee convergence of gradient descent-ascent dynamics |
| topic | Optimization and Control 90C47, 49J35 |
| url | https://arxiv.org/abs/2602.16517 |