Generalized alternating direction method of multipliers: new theoretical insights and applications. Recently, the alternating direction method of multipliers (ADMM) has received intensive attention from a broad spectrum of areas. The generalized ADMM (GADMM) proposed by Eckstein and Bertsekas is an efficient and simple acceleration scheme of ADMM. In this paper, we take a deeper look at the linearized version of GADMM where one of its subproblems is approximated by a linearization strategy. This linearized version is particularly efficient for a number of applications arising from different areas. Theoretically, we show the worst-case $mathcal{O}(1/k)$ convergence rate measured by the iteration complexity ($k$ represents the iteration counter) in both the ergodic and a nonergodic senses for the linearized version of GADMM. Numerically, we demonstrate the efficiency of this linearized version of GADMM by some rather new and core applications in statistical learning. Code packages in Matlab for these applications are also developed.

References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Fang, Ethan X.; Liu, Han; Toh, Kim-Chuan; Zhou, Wen-Xin: Max-norm optimization for robust matrix recovery (2018)
  2. Gao, Bin; Ma, Feng: Symmetric alternating direction method with indefinite proximal regularization for linearly constrained convex optimization (2018)
  3. Zarepisheh, Masoud; Xing, Lei; Ye, Yinyu: A computation study on an integrated alternating direction method of multipliers for large scale optimization (2018)
  4. Bredies, Kristian; Sun, Hongpeng: A proximal point analysis of the preconditioned alternating direction method of multipliers (2017)
  5. Gonçalves, Max L.N.; Melo, Jefferson G.; Monteiro, Renato D.C.: Improved pointwise iteration-complexity of A regularized ADMM and of a regularized non-Euclidean HPE framework (2017)
  6. Liu, Jing; Duan, Yongrui; Sun, Min: A symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming (2017)
  7. Sun, Hongchun; Tian, Maoying; Sun, Min: The symmetric ADMM with indefinite proximal regularization and its application (2017)
  8. Cai, T.Tony; Zhou, Wen-Xin: Matrix completion via max-norm constrained optimization (2016)
  9. He, Bingsheng; Ma, Feng; Yuan, Xiaoming: Convergence study on the symmetric version of ADMM with larger step sizes (2016)
  10. Wang, Yanbo; Liu, Quan; Yuan, Bo: Learning latent variable Gaussian graphical model for biomolecular network with low sample complexity (2016)
  11. Fang, Ethan X.; He, Bingsheng; Liu, Han; Yuan, Xiaoming: Generalized alternating direction method of multipliers: new theoretical insights and applications (2015)