文章基本信息

标题：Generalized alternating direction method of multipliers: new theoretical insights and applications
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作者：Fang, Ethan X. ; He, Bingsheng ; Liu, Han 等
期刊名称：Mathematical Programming Computation
印刷版ISSN：1867-2957
出版年度：2015
页码：149-187
DOI：10.1007/mpc.v0i0.158
语种：English
出版社：Mathematical Programming Computation
摘要：Recently, the alternating direction method of multipliers (ADMM) has received intensive attention from a broad spectrum of areas. The generalized ADMM (GADMM) proposed by Eckstein and Bertsekas is an efficient and simple acceleration scheme of ADMM. In this paper, we take a deeper look at the linearized version of GADMM where one of its subproblems is approximated by a linearization strategy. This linearized version is particularly efficient for a number of applications arising from different areas. Theoretically, we show the worstcase O(1/k) convergence rate measured by the iteration complexity (k represents the iteration counter) in both the ergodic and a nonergodic senses for the linearized version of GADMM. Numerically, we demonstrate the efficiency of this linearized version of GADMM by some rather new and core applications in statistical learning. Code packages in Matlab for these applications are also developed.
关键词：90C25; 90C06; 62J05