KURDYKA-LOJASIEWICZ EXPONENT VIA HADAMARD PARAMETRIZATION

doi:10.1137/24M1636186

	KURDYKA-LOJASIEWICZ EXPONENT VIA HADAMARD PARAMETRIZATION
	Ouyang, Wenqing 1,2; Liu, Yuncheng 3; Pong, Ting Kei 4; Wang, Hao5
	2025
发表期刊	SIAM JOURNAL ON OPTIMIZATION (IF:2.6[JCR-2023],3.2[5-Year])
ISSN	1052-6234
EISSN	1095-7189
卷号	35 期号:1 页码:62-91
发表状态	已发表
DOI	10.1137/24M1636186
摘要	We consider a class of 1-regularized optimization problems and the associated smooth ``overparameterized"" optimization problems built upon the Hadamard parametrization, or equivalently, the Hadamard difference parametrization (HDP). We characterize the set of second-order stationary points of the HDP-based model and show that they correspond to some stationary points of the corresponding 1-regularized model. More importantly, we show that the Kurdyka-Lojasiewicz \ (KL) exponent of the HDP-based model at a second-order stationary point can be inferred from that of the corresponding 1-regularized model under suitable assumptions. Our assumptions are general enough to cover a wide variety of loss functions commonly used in 1-regularized models, such as the least squares loss function and the logistic loss function. Since the KL exponents of many 1-regularized models are explicitly known in the literature, our results allow us to leverage these known exponents to deduce the KL exponents at second-order stationary points of the corresponding HDP-based models, which were previously unknown. Finally, we demonstrate how these explicit KL exponents at second-order stationary points can be applied to deducing the explicit local convergence rate of a standard gradient descent method for minimizing the HDP-based model. © 2025 Society for Industrial and Applied Mathematics.
关键词	Convergence of numerical methods Equivalence classes Gradient methods Hadamard transforms Optimization Hadamard Kurdyka–&lstrok ojasiewicz exponent Overparametrization Parametrizations Property Second orders Second-order stationarity Stationarity Stationary points Strict saddle property
URL	查看原文
收录类别	EI ; SCI
语种	英语
资助项目	Natural Science Founda-tion of Sichuan Province[2022NSFSC1830] ; Southwest Minzu University Research Startup Funds[RQD2022035] ; Hong Kong Research Grants Council[PolyU153001/22p] ; Natural Science Foundation of Shanghai[21ZR1442800]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:001447231800004
出版者	Society for Industrial and Applied Mathematics Publications
EI入藏号	20250317706835
EI主题词	Least squares approximations
EI分类号	1102.1 ; 1201 ; 1201.3 ; 1201.7 ; 1201.9
原始文献类型	Journal article (JA)
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/483868
专题	信息科学与技术学院信息科学与技术学院_PI研究组_王浩组
作者单位	1.School of Data Science (SDS), Shenzhen Research Institute of Big Data (SRIBD), Shenzhen, China; 2.Chinese University of Hong Kong, Hong Kong; 3.School of Mathematics, Southwest Minzu University, Sichuan, Chengdu, China; 4.Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China; 5.School of Information Science and Technology, ShanghaiTech University, Shanghai, China
推荐引用方式 GB/T 7714	Ouyang, Wenqing,Liu, Yuncheng,Pong, Ting Kei,et al. KURDYKA-LOJASIEWICZ EXPONENT VIA HADAMARD PARAMETRIZATION[J]. SIAM JOURNAL ON OPTIMIZATION,2025,35(1):62-91.
APA	Ouyang, Wenqing,Liu, Yuncheng,Pong, Ting Kei,&Wang, Hao.(2025).KURDYKA-LOJASIEWICZ EXPONENT VIA HADAMARD PARAMETRIZATION.SIAM JOURNAL ON OPTIMIZATION,35(1),62-91.
MLA	Ouyang, Wenqing,et al."KURDYKA-LOJASIEWICZ EXPONENT VIA HADAMARD PARAMETRIZATION".SIAM JOURNAL ON OPTIMIZATION 35.1(2025):62-91.