scholarly journals An algorithm combining coordinate descent and split Bregman iterative for fractional image denoising model

2021 ◽  
Vol 15 ◽  
pp. 174830262110311
Author(s):  
Donghong Zhao ◽  
Yonghua Fan ◽  
Haoyu Liu ◽  
Yafeng Yang
Keyword(s):  
Total Variation ◽  
Minimization Problem ◽  
Optimization Problems ◽  
Descent Method ◽  
Coordinate Descent ◽  
Split Bregman ◽  
Coordinate Descent Method ◽  
Total Variation Model ◽  
Split Bregman Algorithm ◽  
Variation Model

The split Bregman algorithm and the coordinate descent method are efficient tools for solving optimization problems, which have been proven to be effective for the total variation model. We propose an algorithm for fractional total variation model in this paper, and employ the coordinate descent method to decompose the fractional-order minimization problem into scalar sub-problems, then solve the sub-problem by using split Bregman algorithm. Numerical results are presented in the end to demonstrate the superiority of the proposed algorithm.

Faster convergence of a randomized coordinate descent method for linearly constrained optimization problems

2018 ◽  
Vol 16 (05) ◽  
pp. 741-755 ◽  
Author(s):  
Qin Fang ◽  
Min Xu ◽  
Yiming Ying
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Descent Method ◽  
Coordinate Descent ◽  
Descent Methods ◽  
Coordinate Descent Method ◽  
Linearly Constrained Optimization ◽  
Main Challenge ◽  
Linearly Constrained ◽  
Coupled Constraints

The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is that the size of data is very large, which makes usual gradient-based methods infeasible. Recently, Necoara, Nesterov and Glineur [Random block coordinate descent methods for linearly constrained optimization over networks, J. Optim. Theory Appl. 173(1) (2017) 227–254] proposed an efficient randomized coordinate descent method to solve this type of optimization problems and presented an appealing convergence analysis. In this paper, we develop new techniques to analyze the convergence of such algorithms, which are able to greatly improve the results presented in the above. This refined result is achieved by extending Nesterov’s second technique [Efficiency of coordinate descent methods on huge-scale optimization problems, SIAM J. Optim. 22 (2012) 341–362] to the general optimization problems with linearly coupled constraints. A novel technique in our analysis is to establish the basis vectors for the subspace of the linear constraints.

scholarly journals On Gradient Descent and Co-ordinate Descent methods and its variants.

2020 ◽  
Vol 19 (3) ◽  
pp. 107-115
Author(s):  
Sajjadul Bari ◽  
Md. Rajib Arefin ◽  
Sohana Jahan
Keyword(s):  
Unconstrained Optimization ◽  
Gradient Descent ◽  
Optimization Problems ◽  
Descent Method ◽  
Coordinate Descent ◽  
Loss Functions ◽  
Descent Methods ◽  
Step Size ◽  
Coordinate Descent Method ◽  
Unconstrained Optimization Problems

This research is focused on Unconstrained Optimization problems. Among a number of methods that can be used to solve Unconstrained Optimization problems we have worked on Gradient and Coordinate Descent methods. Step size plays an important role for optimization. Here we have performed numerical experiment with Gradient and Coordinate Descent method for several step size choices. Comparison between different variants of Gradient and Coordinate Descent methods and their efficiency are demonstrated by implementing in loss functions minimization problem.

Coordinate Descent Method for k-means

2021 ◽  
pp. 1-1
Author(s):  
Feiping Nie ◽  
Jingjing Xue ◽  
Danyang Wu ◽  
Rong Wang ◽  
Hui Li ◽  
...  
Keyword(s):  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method
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