On the \(O(1/K)\) convergence rate of alternating direction method of multipliers in a complex domain

2018 ◽  
Vol 60 ◽  
pp. 95
Author(s):  
Lu Li ◽  
G. Q. Wang ◽  
J. L. Zhang
Keyword(s):  
Convergence Rate ◽  
Alternating Direction Method ◽  
Complex Domain ◽  
Method Of Multipliers ◽  
Alternating Direction

ON THE CONVERGENCE RATE OF THE ALTERNATING DIRECTION METHOD OF MULTIPLIERS IN A COMPLEX DOMAIN

2018 ◽  
Vol 60 (1) ◽  
pp. 95-117 ◽  
Author(s):  
L. LI ◽  
G. Q. WANG ◽  
J. L. ZHANG
Keyword(s):  
Variational Inequality ◽  
Convergence Rate ◽  
Numerical Simulations ◽  
Complex Form ◽  
Alternating Direction Method ◽  
Complex Domain ◽  
Method Of Multipliers ◽  
Alternating Direction ◽  
Wirtinger Calculus ◽  
Real Domain

We focus on the convergence rate of the alternating direction method of multipliers (ADMM) in a complex domain. First, the complex form of variational inequality (VI) is established by using the Wirtinger calculus technique. Second, the $O(1/K)$ convergence rate of the ADMM in a complex domain is provided. Third, the ADMM in a complex domain is applied to the least absolute shrinkage and selectionator operator (LASSO). Finally, numerical simulations are provided to show that ADMM in a complex domain has the $O(1/K)$ convergence rate and that it has certain advantages compared with the ADMM in a real domain.

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.

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