Volume 13, Issue 1
A Fast Symmetric Alternating Direction Method of Multipliers

Gang Luo and Qingzhi Yang

10.4208/nmtma.OA-2018-0108

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 200-219.

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  • 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.

  • History

Published online: 2019-12

  • AMS Subject Headings

90C25, 90C30, 49M29, 65B99

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