http://dx.doi.org/10.1007/s10957-014-0682-8">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Further study on the convergence rate of alternating direction method of multipliers with logarithmic-quadratic proximal regularization

Language

English

Abstract

© 2014, Springer Science+Business Media New York.In the literature, the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization has been proved to be convergent, and its worst-case convergence rate in the ergodic sense has been established. In this paper, we focus on a convex minimization model and consider an inexact version of the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization. Our primary purpose is to further study its convergence rate and to establish its worst-case convergence rates measured by the iteration complexity in both the ergodic and non-ergodic senses. In particular, existing convergence rate results for this combination are subsumed by the new results.

Keywords

Alternating direction method of multipliers, Convergence rate, Convex programming, Iteration complexity, Logarithmic-quadratic proximal

Publication Date

2015

Source Publication Title

Journal of Optimization Theory and Applications

Volume

166

Issue

3

Start Page

906

End Page

929

Publisher

Springer Verlag

ISSN (print)

00223239

ISSN (electronic)

15732878

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