On the O(1/t) Convergence Rate of Alternating Direction Method with Logarithmic-Quadratic Proximal Regularization

Min Tao; Xiaoming Yuan

doi:10.1137/110847639

On the O(1/t) Convergence Rate of Alternating Direction Method with Logarithmic-Quadratic Proximal Regularization

Min Tao
, Xiaoming Yuan^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

38 Citations (Scopus)

51 Downloads (Pure)

Abstract

It was shown recently that the Douglas-Rachford alternating direction method of multipliers can be combined with the logarithmic-quadratic proximal regularization for solving a class of variational inequalities with separable structures. This paper further shows a worst-case O(1/t) convergence rate for this algorithm where a general Glowinski relaxation factor is used.

Original language	English
Pages (from-to)	1431-1448
Number of pages	18
Journal	SIAM Journal on Optimization
Volume	22
Issue number	4
DOIs	https://doi.org/10.1137/110847639
Publication status	Published - 31 Oct 2012

User-Defined Keywords

Alternating direction method of multipliers
Convergence rate
Glowinski's relaxation factor
Logarithmic-quadratic proximal regularization
Variational inequality

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10.1137/110847639

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abstract = "It was shown recently that the Douglas-Rachford alternating direction method of multipliers can be combined with the logarithmic-quadratic proximal regularization for solving a class of variational inequalities with separable structures. This paper further shows a worst-case O(1/t) convergence rate for this algorithm where a general Glowinski relaxation factor is used.",

keywords = "Alternating direction method of multipliers, Convergence rate, Glowinski's relaxation factor, Logarithmic-quadratic proximal regularization, Variational inequality",

author = "Min Tao and Xiaoming Yuan",

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AU - Yuan, Xiaoming

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KW - Alternating direction method of multipliers

KW - Convergence rate

KW - Glowinski's relaxation factor

KW - Logarithmic-quadratic proximal regularization

KW - Variational inequality

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On the O(1/t) Convergence Rate of Alternating Direction Method with Logarithmic-Quadratic Proximal Regularization

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