Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization

Min Li; Xinxin Li; Xiaoming YUAN

doi:10.1007/s10957-014-0567-x

Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization

Min Li, Xinxin Li, Xiaoming YUAN^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	218-233
Number of pages	16
Journal	Journal of Optimization Theory and Applications
Volume	164
Issue number	1
DOIs	https://doi.org/10.1007/s10957-014-0567-x
Publication status	Published - Jan 2014

Scopus Subject Areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

User-Defined Keywords

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

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10.1007/s10957-014-0567-x

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abstract = "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.",

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AB - 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.

KW - Convergence rate

KW - Generalized alternating direction method of multipliers

KW - Logarithmic–quadratic proximal method

KW - Variational inequality

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Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization

Abstract

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