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

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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.

  • Keywords

Convex programming, augmented Lagrangian method, multi-block separable model, Jacobian splitting, unified algorithmic framework.

  • AMS Subject Headings

90C25, 90C30, 90C33

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-36-262, author = {Bingsheng He , }, 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 - Bingsheng He , 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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