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, Xiaokai 2; Yang, Junfeng 1
刊名	PACIFIC JOURNAL OF OPTIMIZATION
	2022
卷号	18 期号:2 页码:497-517
关键词	structured convex optimization primal-dual full-splitting saddle point sublinear convergence rate golden ratio
ISSN号	1348-9151
英文摘要	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.
WOS研究方向	Operations Research & Management Science ; Mathematics
语种	英语
出版者	YOKOHAMA PUBL
WOS记录号	WOS:000797602800001
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/158899]
专题	理学院
作者单位	1.Nanjing Univ, Dept Math, Nanjing, Peoples R China; 2.Lanzhou Univ Technol, Sch Sci, Lanzhou, Gansu, Peoples R China
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.