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Volume 34, Issue 2
A Block-Coordinate Descent Method for Linearly Constrained Minimization Problem

Xuefang Liu & Zheng Peng

Ann. Appl. Math., 34 (2018), pp. 138-152.

Published online: 2022-06

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  • Abstract

In this paper, a block coordinate descent method is developed to solve a linearly constrained separable convex optimization problem. The proposed method divides the decision variable into a few blocks based on certain rules. Then the candidate solution is iteratively obtained by updating one block at each iteration. The problem, whether or not there are overlapping regions between two immediately adjacent blocks, is investigated. The global convergence of the proposed method is established under some suitable assumptions. Numerical results show that the proposed method is effective compared with some “full-type” methods.

  • Keywords

linearly constrained optimization, block coordinate descent, Gauss-Seidel fashion.

  • AMS Subject Headings

90C25, 90C30, 65K10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-34-138, author = {Liu , Xuefang and Peng , Zheng}, title = {A Block-Coordinate Descent Method for Linearly Constrained Minimization Problem}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {34}, number = {2}, pages = {138--152}, abstract = {

In this paper, a block coordinate descent method is developed to solve a linearly constrained separable convex optimization problem. The proposed method divides the decision variable into a few blocks based on certain rules. Then the candidate solution is iteratively obtained by updating one block at each iteration. The problem, whether or not there are overlapping regions between two immediately adjacent blocks, is investigated. The global convergence of the proposed method is established under some suitable assumptions. Numerical results show that the proposed method is effective compared with some “full-type” methods.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20568.html} }
TY - JOUR T1 - A Block-Coordinate Descent Method for Linearly Constrained Minimization Problem AU - Liu , Xuefang AU - Peng , Zheng JO - Annals of Applied Mathematics VL - 2 SP - 138 EP - 152 PY - 2022 DA - 2022/06 SN - 34 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/20568.html KW - linearly constrained optimization, block coordinate descent, Gauss-Seidel fashion. AB -

In this paper, a block coordinate descent method is developed to solve a linearly constrained separable convex optimization problem. The proposed method divides the decision variable into a few blocks based on certain rules. Then the candidate solution is iteratively obtained by updating one block at each iteration. The problem, whether or not there are overlapping regions between two immediately adjacent blocks, is investigated. The global convergence of the proposed method is established under some suitable assumptions. Numerical results show that the proposed method is effective compared with some “full-type” methods.

Xuefang Liu & Zheng Peng. (2022). A Block-Coordinate Descent Method for Linearly Constrained Minimization Problem. Annals of Applied Mathematics. 34 (2). 138-152. doi:
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