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arXiv · 2205.00064

A nearly linearly convergent first-order method for nonsmooth functions with quadratic growth

Damek Davis·Liwei Jiang
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Abstract

Classical results show that gradient descent converges linearly to minimizers of smooth strongly convex functions. A natural question is whether there exists a locally nearly linearly convergent method for nonsmooth functions with quadratic growth. This work designs such a method for a wide class of nonsmooth and nonconvex locally Lipschitz functions, including max-of-smooth, Shapiro's decomposable class, and generic semialgebraic functions. The algorithm is parameter-free and derives from Goldstein's conceptual subgradient method.

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Damek Davis, Liwei Jiang. 2022-04-29. A nearly linearly convergent first-order method for nonsmooth functions with quadratic growth. https://arxiv.org/abs/2205.00064

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