A NEW PRIMAL-DUAL ALGORITHM FOR STRUCTURED CONVEX OPTIMIZATION INVOLVING A LIPSCHITZIAN TERM

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	A NEW PRIMAL-DUAL ALGORITHM FOR STRUCTURED CONVEX OPTIMIZATION INVOLVING A LIPSCHITZIAN TERM
	Zhou, Danqing 1; Chang, Xiaokai2 ; Yang, Junfeng 1
	2022
发表期刊	PACIFIC JOURNAL OF OPTIMIZATION
ISSN	1348-9151
卷号	18 期号:2 页码:497-517
摘要	We propose and analyze a golden ratio primal-dual algorithm for solving structured optimization problems involving the sum of three convex terms - a smooth function with Lipschitzian gradient and two nonsmooth proximal-friendly functions, one of which is composed with a linear mapping. The proposed algorithm is of primal-dual and full-splitting type as it solves the primal and the dual problems simultaneously and does not rely on solving any subproblems or linear system of equations iteratively, the smooth function is handled by gradient evaluation, and the nonsmooth functions are handled by their proximity operators. Several well-known algorithms are closely related, e.g., the classical Arrow-Hurwicz method and the primal-dual algorithm of Chambolle and Pock. In particular, it extends the golden ratio primal-dual algorithm recently proposed by Chang and Yang by including an extra smooth term with Lipschitzian gradient. The convergence rates O(1/N) and O(1/N-2) are established for convex and strongly convex cases, respectively, which differentiate themselves from existing results in terms of the adopted optimality measures. Specifically, to measure optimality, most existing results adopt the primal-dual gap function, a major flaw of which is that it could vanish at nonstationary points. In comparison, we adopt function value residual and feasibility violation as optimality measures, which are conventional for 'constrained optimization. Finally, preliminary numerical results on image reconstruction and elastic net regularization problems are presented to demonstrate the efficiency of the proposed algorithm.
关键词	structured convex optimization primal-dual full-splitting saddle point sublinear convergence rate golden ratio
收录类别	SCIE
语种	英语
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000797602800001
出版者	YOKOHAMA PUBL
来源库	WOS
引用统计	被引频次[WOS]：0 [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://ir.lut.edu.cn/handle/2XXMBERH/158899
专题	理学院
通讯作者	Yang, Junfeng
作者单位	1.Nanjing Univ, Dept Math, Nanjing, Peoples R China; 2.Lanzhou Univ Technol, Sch Sci, Lanzhou, Gansu, Peoples R China
第一作者单位	理学院
通讯作者单位	理学院
第一作者的第一单位	理学院
推荐引用方式 GB/T 7714	Zhou, Danqing,Chang, Xiaokai,Yang, Junfeng. A NEW PRIMAL-DUAL ALGORITHM FOR STRUCTURED CONVEX OPTIMIZATION INVOLVING A LIPSCHITZIAN TERM[J]. PACIFIC JOURNAL OF OPTIMIZATION,2022,18(2):497-517.
APA	Zhou, Danqing,Chang, Xiaokai,&Yang, Junfeng.(2022).A NEW PRIMAL-DUAL ALGORITHM FOR STRUCTURED CONVEX OPTIMIZATION INVOLVING A LIPSCHITZIAN TERM.PACIFIC JOURNAL OF OPTIMIZATION,18(2),497-517.
MLA	Zhou, Danqing,et al."A NEW PRIMAL-DUAL ALGORITHM FOR STRUCTURED CONVEX OPTIMIZATION INVOLVING A LIPSCHITZIAN TERM".PACIFIC JOURNAL OF OPTIMIZATION 18.2(2022):497-517.