GOLDEN RATIO PRIMAL-DUAL ALGORITHM WITH LINESEARCH

doi:10.1137/21M1420319

CORC > 兰州理工大学 > 兰州理工大学 > 理学院

	GOLDEN RATIO PRIMAL-DUAL ALGORITHM WITH LINESEARCH
	Chang, Xiao-kai 2; Yang, Junfeng 3; Zhang, Hongchao 1
刊名	SIAM JOURNAL ON OPTIMIZATION
	2022
卷号	32 期号:3 页码:1584-1613
关键词	saddle point problem golden ratio primal-dual algorithm linesearch acceleration ergodic sublinear convergence linear convergence
ISSN号	1052-6234
DOI	10.1137/21M1420319
英文摘要	The golden ratio primal-dual algorithm (GRPDA) is a new variant of the classical Arrow-Hurwicz method for solving structured convex optimization problems, in which the objective function consists of the sum of two closed proper convex functions, one of which involves a composi-tion with a linear transform. The same as the Arrow-Hurwicz method and the popular primal-dual algorithm (PDA) of Chambolle and Pock, GRPDA is full-splitting in the sense that it does not rely on solving any subproblems or linear system of equations iteratively. Compared with PDA, an im-portant feature of GRPDA is that it permits larger primal and dual stepsizes. However, the stepsize condition of GRPDA requires that the spectral norm of the linear transform is known, which can be difficult to obtain in some applications. Furthermore, constant stepsizes are usually overconservative in practice. In this paper, we propose a linesearch strategy for GRPDA, which not only does not require the spectral norm of the linear transform but also allows adaptive and potentially much larger stepsizes. Within each linesearch step, only the dual variable needs to be updated, and it is thus quite cheap and does not require any extra matrix-vector multiplications for many special yet important applications such as a regularized least-squares problem. Global iterate convergence and O(1/N) ergodic convergence rate results, measured by the function value gap and constraint viola-tions of an equivalent optimization problem, are established, where N denotes the iteration counter. When one of the component functions is strongly convex, faster O(1/N2) ergodic convergence rate results, quantified by the same measures, are established by adaptively choosing some algorithmic parameters. Moreover, when the subdifferential operators of the component functions are strongly metric subregular, a condition that is much weaker than strong convexity, we show that the iterates converge R-linearly to the unique solution. Numerical experiments on matrix game and LASSO problems illustrate the effectiveness of the proposed linesearch strategy.
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000834106000004
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/159473]
专题	理学院
作者单位	1.Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA 2.Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Gansu, Peoples R China; 3.Nanjing Univ, Dept Math, Peoples Republ China, Nanjing 210093, Peoples R China;
推荐引用方式 GB/T 7714	Chang, Xiao-kai,Yang, Junfeng,Zhang, Hongchao. GOLDEN RATIO PRIMAL-DUAL ALGORITHM WITH LINESEARCH[J]. SIAM JOURNAL ON OPTIMIZATION,2022,32(3):1584-1613.
APA	Chang, Xiao-kai,Yang, Junfeng,&Zhang, Hongchao.(2022).GOLDEN RATIO PRIMAL-DUAL ALGORITHM WITH LINESEARCH.SIAM JOURNAL ON OPTIMIZATION,32(3),1584-1613.
MLA	Chang, Xiao-kai,et al."GOLDEN RATIO PRIMAL-DUAL ALGORITHM WITH LINESEARCH".SIAM JOURNAL ON OPTIMIZATION 32.3(2022):1584-1613.