scholarly journals An alternating direction method of multipliers with a worst-case $O(1/n^2)$ convergence rate

2018 ◽  
Vol 88 (318) ◽  
pp. 1685-1713 ◽  
Author(s):  
Wenyi Tian ◽  
Xiaoming Yuan
Keyword(s):  
Convergence Rate ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Worst Case ◽  
Alternating Direction

scholarly journals A Dynamical Alternating Direction Multiplier Method for Two-Block Optimization Problems

2021 ◽  
Author(s):  
Miantao Chao ◽  
Liqun Liu
Keyword(s):  
Dynamical System ◽  
Optimization Problems ◽  
Suitable Condition ◽  
Time Discretization ◽  
Alternating Direction Method ◽  
Lagrangian Function ◽  
Method Of Multipliers ◽  
Worst Case ◽  
Alternating Direction ◽  
Separable Optimization

Abstract In this paper, we propose a dynamic alternating direction method of multipliers for two-block separable optimization problems. The well-known classical ADMM can be obtained after the time discretization of the dynamical system. Under suitable condition, we prove that the trajectory asymptotically converges to a saddle point of the Lagrangian function of the problems. When the coefficient matrices in the constraint are identiy matrices, we prove the worst-case O(1/t) convergence rate in ergodic sense.

Image denoising algorithm of compressed sensing based on alternating direction method of multipliers

2021 ◽  
pp. 2250009
Author(s):  
Changjie Fang ◽  
Jingyu Chen ◽  
Shenglan Chen
Keyword(s):  
Compressed Sensing ◽  
Convergence Rate ◽  
Objective Function ◽  
Image Denoising ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Alternating Direction ◽  
Time Simulation ◽  
Optimal Value ◽  
Simulation Results

In this paper, we propose an image denoising algorithm for compressed sensing based on alternating direction method of multipliers (ADMM). We prove that the objective function of the iterates approaches the optimal value. We also prove the [Formula: see text] convergence rate of our algorithm in the ergodic sense. At the same time, simulation results show that our algorithm is more efficient in image denoising compared with existing methods.

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.

Sign in / Sign up

Export Citation Format

Share Document