Computing Kurdyka-Łojasiewicz exponents via composition and symmetry
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910044717580288 |
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| author | Josz, Cédric Ouyang, Wenqing |
| author_facet | Josz, Cédric Ouyang, Wenqing |
| contents | We devise calculus rules for the Kurdyka-Łojasiewicz exponent using the rank theorem and Lie group actions. They apply to a wide class of composite and invariant functions, and are particularly suitable for handling nonisolated local minima. Notably, smoothness plays no role, eschewing gradient and Hessian computations. This provides a unified framework for establishing linear convergence of various algorithms in matrix factorization, $\ell_1$-matrix factorization, matrix sensing, and linear neural networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing Kurdyka-Łojasiewicz exponents via composition and symmetry Josz, Cédric Ouyang, Wenqing Optimization and Control 32B20, 49J53, 53-XX We devise calculus rules for the Kurdyka-Łojasiewicz exponent using the rank theorem and Lie group actions. They apply to a wide class of composite and invariant functions, and are particularly suitable for handling nonisolated local minima. Notably, smoothness plays no role, eschewing gradient and Hessian computations. This provides a unified framework for establishing linear convergence of various algorithms in matrix factorization, $\ell_1$-matrix factorization, matrix sensing, and linear neural networks. |
| title | Computing Kurdyka-Łojasiewicz exponents via composition and symmetry |
| topic | Optimization and Control 32B20, 49J53, 53-XX |
| url | https://arxiv.org/abs/2602.22553 |