Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

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

Language

English

Abstract

© 2015, Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society.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 worst-case $${\mathcal {O}}(1/k)$$O(1/k) convergence rate measured by the iteration complexity ($$k$$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.

Keywords

Alternating direction method of multipliers, Convergence rate, Convex optimization, Discriminant analysis, Statistical learning, Variable selection

Publication Date

2015

Source Publication Title

Mathematical Programming Computation

Volume

7

Issue

2

Start Page

149

End Page

187

Publisher

Springer Verlag

DOI

10.1007/s12532-015-0078-2

Link to Publisher's Edition

http://dx.doi.org/10.1007/s12532-015-0078-2

ISSN (print)

18672949

ISSN (electronic)

18672957

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