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A Fast Symmetric Alternating Direction Method of Multipliers

A Fast Symmetric Alternating Direction Method of Multipliers

Year:    2020

Author:    Qingzhi Yang, Gang Luo, Qingzhi Yang

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 1 : pp. 200–219

Abstract

In recent years, alternating direction method of multipliers (ADMM) and its variants are popular for the extensive use in image processing and statistical learning. A variant of ADMM: symmetric ADMM, which updates the Lagrange multiplier twice in one iteration, is always faster whenever it converges. In this paper, combined with Nesterov's accelerating strategy, an accelerated symmetric ADMM is proposed. We prove its $\mathcal{O}(\frac{1}{k^2})$ convergence rate under strongly convex condition. For the general situation, an accelerated method with a restart rule is proposed. Some preliminary numerical experiments show the efficiency of our algorithms.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2018-0108

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 1 : pp. 200–219

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Nesterov's accelerating strategy alternating direction method of multipliers symmetric ADMM separable linear constrained optimization.

Author Details

Qingzhi Yang

Gang Luo

Qingzhi Yang

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