1. Global stability of first-order methods for coercive tame functions.
- Author
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Josz, Cédric and Lai, Lexiao
- Subjects
- *
SUBGRADIENT methods , *DIFFERENTIAL inclusions , *POINT set theory , *GEOMETRY , *NEIGHBORHOODS - Abstract
We consider first-order methods with constant step size for minimizing locally Lipschitz coercive functions that are tame in an o-minimal structure on the real field. We prove that if the method is approximated by subgradient trajectories, then the iterates eventually remain in a neighborhood of a connected component of the set of critical points. Under suitable method-dependent regularity assumptions, this result applies to the subgradient method with momentum, the stochastic subgradient method with random reshuffling and momentum, and the random-permutations cyclic coordinate descent method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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