GADMM

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 23 articles , 1 standard article )

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  1. Adona, V. A.; Gonçalves, M. L. N.; Melo, J. G.: An inexact proximal generalized alternating direction method of multipliers (2020)
  2. Gonçalves, Max L. N.; Melo, Jefferson G.; Monteiro, Renato D. C.: On the iteration-complexity of a non-Euclidean hybrid proximal extragradient framework and of a proximal ADMM (2020)
  3. Adona, V. A.; Gonçalves, M. L. N.; Melo, J. G.: Iteration-complexity analysis of a generalized alternating direction method of multipliers (2019)
  4. Adona, Vando A.; Gonçalves, Max L. N.; Melo, Jefferson G.: A partially inexact proximal alternating direction method of multipliers and its iteration-complexity analysis (2019)
  5. Baake, Michael; Frank, Natalie Priebe; Grimm, Uwe; Robinson, E. Arthur jun.: Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction (2019)
  6. Sun, Hongpeng: Analysis of fully preconditioned alternating direction method of multipliers with relaxation in Hilbert spaces (2019)
  7. Fang, Ethan X.; Liu, Han; Toh, Kim-Chuan; Zhou, Wen-Xin: Max-norm optimization for robust matrix recovery (2018)
  8. Gao, Bin; Ma, Feng: Symmetric alternating direction method with indefinite proximal regularization for linearly constrained convex optimization (2018)
  9. Gonçalves, Max L. N.; Marques Alves, Maicon; Melo, Jefferson G.: Pointwise and ergodic convergence rates of a variable metric proximal alternating direction method of multipliers (2018)
  10. Gonçalves, M. L. N.: On the pointwise iteration-complexity of a dynamic regularized ADMM with over-relaxation stepsize (2018)
  11. Liang, Xiaobo; Bai, Jianchao: Preconditioned ADMM for a class of bilinear programming problems (2018)
  12. Liu, Yongchao; Yuan, Xiaoming; Zeng, Shangzhi; Zhang, Jin: Partial error bound conditions and the linear convergence rate of the alternating direction method of multipliers (2018)
  13. Tao, Min; Yuan, Xiaoming: On the optimal linear convergence rate of a generalized proximal point algorithm (2018)
  14. Tao, Min; Yuan, Xiaoming: The generalized proximal point algorithm with step size 2 is not necessarily convergent (2018)
  15. Zarepisheh, Masoud; Xing, Lei; Ye, Yinyu: A computation study on an integrated alternating direction method of multipliers for large scale optimization (2018)
  16. Bredies, Kristian; Sun, Hongpeng: A proximal point analysis of the preconditioned alternating direction method of multipliers (2017)
  17. 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)
  18. Liu, Jing; Duan, Yongrui; Sun, Min: A symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming (2017)
  19. Sun, Hongchun; Tian, Maoying; Sun, Min: The symmetric ADMM with indefinite proximal regularization and its application (2017)
  20. Cai, T. Tony; Zhou, Wen-Xin: Matrix completion via max-norm constrained optimization (2016)

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