STOCHASTIC OPTIMIZATION OVER PROXIMALLY SMOOTH SETS

被引：0
|
作者：
Davis, Damek [1 ]
Drusvyatskiy, Dmitriy [2 ]
Shi, Zhan [2 ]
机构：
[1] Cornell Univ, Sch ORIE, Ithaca, NY 14850 USA
[2] Univ Washington, Dept Math, Seattle, WA 98195 USA
来源：
SIAM JOURNAL ON OPTIMIZATION | 2025年 / 35卷 / 01期
关键词：
stochastic; subgradient; proximal; weakly convex; proximally smooth; LOCALLY LIPSCHITZ FUNCTIONS; WEAKLY CONVEX-OPTIMIZATION; PROX-REGULARITY; ALGORITHM; MINIMIZATION; CONVERGENCE; NONSMOOTH; COMPOSITE; MODEL;
D O I：
10.1137/20M1320225
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along with a retraction operation to restore feasibility. All the proposed methods come equipped with a finite time efficiency guarantee in terms of a natural stationarity measure. We discuss consequences for nonsmooth optimization over smooth manifolds and over sets cut out by weakly convex inequalities.
引用
收藏
页码：157 / 179
页数：23
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