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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Convergence analysis of the generalized alternating direction method of multipliers with logarithmic–quadratic proximal regularization

Language

English

Abstract

© 2014, Springer Science+Business Media New York. We consider combining the generalized alternating direction method of multipliers, proposed by Eckstein and Bertsekas, with the logarithmic–quadratic proximal method proposed by Auslender, Teboulle, and Ben-Tiba for solving a variational inequality with separable structures. For the derived algorithm, we prove its global convergence and establish its worst-case convergence rate measured by the iteration complexity in both the ergodic and nonergodic senses.

Keywords

Convergence rate, Generalized alternating direction method of multipliers, Logarithmic–quadratic proximal method, Variational inequality

Publication Date

2015

Source Publication Title

Journal of Optimization Theory and Applications

Volume

164

Issue

1

Start Page

218

End Page

233

Publisher

Springer Verlag

ISSN (print)

00223239

ISSN (electronic)

15732878

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