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 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.
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References in zbMATH (referenced in 29 articles , 1 standard article )
Showing results 1 to 20 of 29.
Sorted by year (- Xiao, Zhen; Zhang, Qi: Dimension reduction for block-missing data based on sparse sliced inverse regression (2022)
- Xu, Jiawei; Chao, Miantao: An inertial Bregman generalized alternating direction method of multipliers for nonconvex optimization (2022)
- Dolgopolik, Maksim V.: The alternating direction method of multipliers for finding the distance between ellipsoids (2021)
- Yang, Yixuan; Tang, Yuchao; Wen, Meng; Zeng, Tieyong: Preconditioned Douglas-Rachford type primal-dual method for solving composite monotone inclusion problems with applications (2021)
- Adona, V. A.; Gonçalves, M. L. N.; Melo, J. G.: An inexact proximal generalized alternating direction method of multipliers (2020)
- 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)
- Jiang, Fan; Wu, Zhongming; Cai, Xingju: Generalized ADMM with optimal indefinite proximal term for linearly constrained convex optimization (2020)
- Adona, V. A.; Gonçalves, M. L. N.; Melo, J. G.: Iteration-complexity analysis of a generalized alternating direction method of multipliers (2019)
- 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)
- 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)
- Sun, Hongpeng: Analysis of fully preconditioned alternating direction method of multipliers with relaxation in Hilbert spaces (2019)
- Wu, Tingting; Zhang, Wenxing; Wang, David Z. W.; Sun, Yuehong: An efficient Peaceman-Rachford splitting method for constrained TGV-shearlet-based MRI reconstruction (2019)
- Fang, Ethan X.; Liu, Han; Toh, Kim-Chuan; Zhou, Wen-Xin: Max-norm optimization for robust matrix recovery (2018)
- Gao, Bin; Ma, Feng: Symmetric alternating direction method with indefinite proximal regularization for linearly constrained convex optimization (2018)
- 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)
- Gonçalves, M. L. N.: On the pointwise iteration-complexity of a dynamic regularized ADMM with over-relaxation stepsize (2018)
- Liang, Xiaobo; Bai, Jianchao: Preconditioned ADMM for a class of bilinear programming problems (2018)
- 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)
- Tao, Min; Yuan, Xiaoming: The generalized proximal point algorithm with step size 2 is not necessarily convergent (2018)
- Tao, Min; Yuan, Xiaoming: On the optimal linear convergence rate of a generalized proximal point algorithm (2018)