A partially proximal linearized alternating minimization method for finding Dantzig selectors

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Xiaoyu Mao ◽  
Hongjin He ◽  
Hong-Kun Xu
Keyword(s):  
Alternating Minimization ◽  
Minimization Method ◽  
Alternating Minimization Method

scholarly journals A hybrid regularizers model for multiplicative noise removal

2021 ◽  
pp. 40-50
Author(s):  
Thi Thu Thao Tran ◽  
Cong Thang Pham ◽  
Duc Hong Vo ◽  
Duc Hoang Vo
Keyword(s):  
Variational Method ◽  
Minimization Problem ◽  
Existence And Uniqueness ◽  
Multiplicative Noise ◽  
State Of The Art ◽  
Noise Removal ◽  
Alternating Minimization ◽  
Minimization Method ◽  
Multiplicative Noise Removal ◽  
Alternating Minimization Method

In this paper, we propose a variational method for restoring images corrupted by multiplicative noise. Computationally, we employ the alternating minimization method to solve our minimization problem. We also study the existence and uniqueness of the proposed problem. Finally, experimental results are provided to demonstrate the superiority of our proposed hybrid model and algorithm for image denoising in comparison with state-of-the-art methods.

The Analysis of Alternating Minimization Method for Double Sparsity Constrained Optimization Problem

2020 ◽  
Vol 37 (04) ◽  
pp. 2040002
Author(s):  
Huan Gao ◽  
Yingyi Li ◽  
Haibin Zhang
Keyword(s):  
Objective Function ◽  
Rate Of Convergence ◽  
Decision Variable ◽  
Alternating Minimization ◽  
Minimization Method ◽  
Linear Rate ◽  
Iterative Thresholding ◽  
Constrained Minimization Problem ◽  
Sparsity Constrained Optimization ◽  
Alternating Minimization Method

This work analyzes the alternating minimization (AM) method for solving double sparsity constrained minimization problem, where the decision variable vector is split into two blocks. The objective function is a separable smooth function in terms of the two blocks. We analyze the convergence of the method for the non-convex objective function and prove a rate of convergence of the norms of the partial gradient mappings. Then, we establish a non-asymptotic sub-linear rate of convergence under the assumption of convexity and the Lipschitz continuity of the gradient of the objective function. To solve the sub-problems of the AM method, we adopt the so-called iterative thresholding method and study their analytical properties. Finally, some future works are discussed.

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