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math.OC2023
Global stability of first-order methods for coercive tame functions
Cédric Josz, Lexiao Lai
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…
math.OC2023
Convergence of the momentum method for semialgebraic functions with locally Lipschitz gradients
Cédric Josz, Lexiao Lai, Xiaopeng Li
We propose a new length formula that governs the iterates of the momentum method when minimizing differentiable semialgebraic functions with locally Lipschitz gradients. It enables…