THE LEVEL-SET SUBDIFFERENTIAL ERROR BOUND VIA MOREAU ENVELOPES

被引：1

作者：

Wang, Yu ^{[1
]}

Li, Shengjie ^{[1
]}

Li, Minghua ^{[2
]}

Li, Xiaobing ^{[3
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing, Peoples R China

[2] Chongqing Univ Arts & Sci, Key Lab Complex Data Anal & Artificial Intelligen, Chongqing, Peoples R China

[3] Chongqing Jiaotong Univ, Coll Math & Stat, Chongqing, Peoples R China

来源：

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS | 2024年 / 8卷 / 03期

基金：

中国国家自然科学基金;

关键词：

The Kurdyka-ojasiewicz property; Level-set subdifferential error bound; Local Hodlder error bound; Moreau envelope; DESCENT METHODS; CONVERGENCE;

D O I：

10.23952/jnva.8.2024.3.05

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The level -set subdifferential error bound (LSEB) is weaker than the Kurdyka-ojasiewicz (KL) property and can replace it to establish linear convergence for various first -order algorithms. In this paper, we mainly study the behaviour of the level -set subdifferential error bound via Moreau envelopes under suitable assumptions. We provide an example that the Moreau envelope does not have the KL property but has the LSEB when the original function does not satisfy the KL property but only the LSEB.

引用

页码：419 / 431

页数：13

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