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arXiv · 2308.00899

Global stability of first-order methods for coercive tame functions

Cédric Josz·Lexiao Lai
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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.

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Cédric Josz, Lexiao Lai. 2023-08-02. Global stability of first-order methods for coercive tame functions. https://arxiv.org/abs/2308.00899

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