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Volume 36, Issue 3
Study on the Splitting Methods for Separable Convex Optimization in a Unified Algorithmic Framework

Bingsheng He

Anal. Theory Appl., 36 (2020), pp. 262-282.

Published online: 2020-09

[An open-access article; the PDF is free to any online user.]

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  • Abstract

It is well recognized the convenience of converting the linearly constrained convex optimization problems to a monotone variational inequality. Recently, we have proposed a unified algorithmic framework which can guide us to construct the solution methods for solving these monotone variational inequalities. In this work, we revisit two full Jacobian decomposition of the augmented Lagrangian methods for separable convex programming which we have studied a few years ago. In particular, exploiting this framework, we are able to give a very clear and elementary proof of the convergence of these solution methods.

  • AMS Subject Headings

90C25, 90C30, 90C33

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hebma@nju.edu.cn (Bingsheng He)

  • BibTex
  • RIS
  • TXT
@Article{ATA-36-262, author = {He , Bingsheng}, title = {Study on the Splitting Methods for Separable Convex Optimization in a Unified Algorithmic Framework}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {36}, number = {3}, pages = {262--282}, abstract = {

It is well recognized the convenience of converting the linearly constrained convex optimization problems to a monotone variational inequality. Recently, we have proposed a unified algorithmic framework which can guide us to construct the solution methods for solving these monotone variational inequalities. In this work, we revisit two full Jacobian decomposition of the augmented Lagrangian methods for separable convex programming which we have studied a few years ago. In particular, exploiting this framework, we are able to give a very clear and elementary proof of the convergence of these solution methods.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-SU13}, url = {http://global-sci.org/intro/article_detail/ata/18286.html} }
TY - JOUR T1 - Study on the Splitting Methods for Separable Convex Optimization in a Unified Algorithmic Framework AU - He , Bingsheng JO - Analysis in Theory and Applications VL - 3 SP - 262 EP - 282 PY - 2020 DA - 2020/09 SN - 36 DO - http://doi.org/10.4208/ata.OA-SU13 UR - https://global-sci.org/intro/article_detail/ata/18286.html KW - Convex programming, augmented Lagrangian method, multi-block separable model, Jacobian splitting, unified algorithmic framework. AB -

It is well recognized the convenience of converting the linearly constrained convex optimization problems to a monotone variational inequality. Recently, we have proposed a unified algorithmic framework which can guide us to construct the solution methods for solving these monotone variational inequalities. In this work, we revisit two full Jacobian decomposition of the augmented Lagrangian methods for separable convex programming which we have studied a few years ago. In particular, exploiting this framework, we are able to give a very clear and elementary proof of the convergence of these solution methods.

Bingsheng He. (2020). Study on the Splitting Methods for Separable Convex Optimization in a Unified Algorithmic Framework. Analysis in Theory and Applications. 36 (3). 262-282. doi:10.4208/ata.OA-SU13
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