Global stability of first-order methods for coercive tame functions
Mathematical Programming(2023)
摘要
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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关键词
Differential inclusions,Kurdyka–Łojasiewicz inequality,Semi-algebraic geometry
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