Proximal Methods Avoid Active Strict Saddles of Weakly Convex Functions

Davis Damek; Drusvyatskiy Dmitriy

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Proximal Methods Avoid Active Strict Saddles of Weakly Convex Functions

机译：Proximal Methods Avoid Active Strict Saddles of Weakly Convex Functions

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摘要

We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We argue that the strict saddle property may be a realistic assumption in applications, since it provably holds for generic semi-algebraic optimization problems.

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来源
《Foundations of computational mathematics》 |2022年第2期|561-606|共46页
作者
Davis Damek; Drusvyatskiy Dmitriy;
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作者单位

Cornell Univ;

Univ Washington;

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原文格式 PDF
正文语种英语
中图分类应用数学;
关键词
Strict saddle; Proximal gradient; Proximal point; Center stable manifold theorem; Semi-algebraic; FINITE CONVERGENCE; GRADIENT METHODS; DESCENT METHODS; IDENTIFICATION; COMPOSITE; ALGORITHMS;

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Proximal Methods Avoid Active Strict Saddles of Weakly Convex Functions

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