Generalized alternating direction method of multipliers: new theoretical insights and applications

  • 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.

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Metadaten
Author:Ethan X. Fang, Bingsheng He, Han Liu, Xiaoming Yuan
DOI:https://doi.org/10.1007/s12532-015-0078-2
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2015
Tag:Software; Theoretical Computer Science
Volume:7
Issue:2
Page Number:39
First Page:149
Last Page:187
Mathematical Programming Computation :MPC 2015 - Issue 2
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