A Homotopy Alternating Direction Method of Multipliers for Linearly Constrained Separable Convex Optimization

2017 ◽  
Vol 5 (2) ◽  
pp. 271-290 ◽  
Author(s):  
Jiao Yang ◽  
Yi-Qing Dai ◽  
Zheng Peng ◽  
Jie-Peng Zhuang ◽  
Wen-Xing Zhu
Keyword(s):  
Convex Optimization ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Alternating Direction ◽  
Separable Convex Optimization ◽  
Linearly Constrained

scholarly journals Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Variables

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Lu Li ◽  
Xingyu Wang ◽  
Guoqiang Wang
Keyword(s):  
Convex Optimization ◽  
Complex Variables ◽  
Alternating Direction Method ◽  
Projection Algorithm ◽  
Real Field ◽  
Method Of Multipliers ◽  
The Real ◽  
Alternating Direction ◽  
Separable Convex Optimization ◽  
Real Functions

The alternating direction method of multipliers (ADMM) has been widely explored due to its broad applications, and its convergence has been gotten in the real field. In this paper, an ADMM is presented for separable convex optimization of real functions in complex variables. First, the convergence of the proposed method in the complex domain is established by using the Wirtinger Calculus technique. Second, the basis pursuit (BP) algorithm is given in the form of ADMM in which the projection algorithm and the soft thresholding formula are generalized from the real case. The numerical simulations on the reconstruction of electroencephalogram (EEG) signal are provided to show that our new ADMM has better behavior than the classic ADMM for solving separable convex optimization of real functions in complex variables.

A Linearized Alternating Direction Method of Multipliers with Substitution Procedure

2015 ◽  
Vol 32 (03) ◽  
pp. 1550011 ◽  
Author(s):  
Miantao Chao ◽  
Caozong Cheng ◽  
Haibin Zhang
Keyword(s):  
Alternating Direction Method ◽  
Convex Programming Problem ◽  
Method Of Multipliers ◽  
Worst Case ◽  
Alternating Direction ◽  
Separable Convex Programming ◽  
Contractive Type ◽  
Linearly Constrained ◽  
Contraction Type ◽  
Substitution Procedure

We consider the linearly constrained separable convex programming problem whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method of multipliers (ADMM) has been well studied in the literature for the special case m = 2, but the direct extension of ADMM for the general case m ≥ 2 is not necessarily convergent. In this paper, we propose a new linearized ADMM-based contraction type algorithms for the general case m ≥ 2. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case O(1/t) convergence rate in ergodic sense. Finally, numerical results are reported to demonstrate the effectiveness of the proposed algorithm.

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