Abstract
In this paper, we propose a penalty dual-primal balanced-based augmented Lagrangian method for solving linearly constrained convex minimization problems. Convergence and convergence rate of the penalty dual-primal balanced-based augmented Lagrangian method are established by the tool of variational inequality. Further, we generalize the penalty dual-primal balanced-based augmented Lagrangian method to solve linearly constrained multi-block separable convex minimization problems with full splitting technique and partial splitting technique. Numerical results on the basic pursuit problem and the Lasso model are presented to illustrate the efficiency of the proposed methods.
Funding Statement
This research was partially supported by the Natural Science Foundation of China (12071379, 12361062, 62366001), the Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0925, cstc2022ycjh-bgzxm0097), and Natural Science Foundation of Ningxia Provincial of China (2023AAC02053), the Youth Project of Science and Technology Research Program of Chongqing Education Commission of China (KJQN202201802) and the Major Project of Science and Technology Research Program of Chongqing Education Commission of China.
Acknowledgments
The authors would like to express their sincere thanks to the editor and referees for the valuable comments and helpful suggestions, which help to improve the paper. They also would like to express their sincere thanks to Prof. Bingsheng He and Prof. Xiaoming Yuan [16] for their contributions in ALM and its variants as well as balanced technique, which inspires the paper.
Citation
Xiaoqing Ou. Guolin Yu. Jie Liu. Jiawei Chen. Zhaohan Liu. "A New Penalty Dual-primal Augmented Lagrangian Method and its Extensions." Taiwanese J. Math. Advance Publication 1 - 22, 2024. https://doi.org/10.11650/tjm/240603
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