A Local Nearly Linearly Convergent First-Order Method for Nonsmooth Functions with Quadratic Growth.
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| Title: | A Local Nearly Linearly Convergent First-Order Method for Nonsmooth Functions with Quadratic Growth. |
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| Authors: | Davis, Damek1 (AUTHOR) dsd95@cornell.edu, Jiang, Liwei1 (AUTHOR) |
| Source: | Foundations of Computational Mathematics. Jun2025, Vol. 25 Issue 3, p943-1024. 82p. |
| Subjects: | Subgradient methods, Convex functions, Algorithms |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 16153375 |
| DOI: | 10.1007/s10208-024-09653-y |
