An Inexact Golden Ratio Primal-Dual Algorithm for a Saddle Point Problem

Jinxiu Liu, Changjie Fang, Jingtao Qiu
Proceedings of 2025 2nd International Conference on Machine Learning and Intelligent Computing, PMLR 278:427-433, 2025.

Abstract

Convex optimization problems have wide applications in many fields such as mathematics, finance, industrial engineering, and management science. The primal dual algorithm (PDA), which is a classical approach for tackling a certain class of convex-concave saddle point problems, still has shortcomings such as fixed step size and difficulty in accurately solving certain subproblems. Therefore, designing more efficient inexact algorithms to solve these problems has important practical significance. During this investigation, we introduce an inexact golden ratio primal-dual algorithm based on the absolute error criteria of non-negative summable sequences. We establish the global convergence and the $O(1/N)$ rate of convergence for the proposed inexact algorithm, and the effectiveness of the proposed algorithm is verified by the image restoration experiment.

Cite this Paper

BibTeX
@InProceedings{pmlr-v278-liu25e, title = {An Inexact Golden Ratio Primal-Dual Algorithm for a Saddle Point Problem}, author = {Liu, Jinxiu and Fang, Changjie and Qiu, Jingtao}, booktitle = {Proceedings of 2025 2nd International Conference on Machine Learning and Intelligent Computing}, pages = {427--433}, year = {2025}, editor = {Zeng, Nianyin and Pachori, Ram Bilas and Wang, Dongshu}, volume = {278}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v278/main/assets/liu25e/liu25e.pdf}, url = {https://proceedings.mlr.press/v278/liu25e.html}, abstract = {Convex optimization problems have wide applications in many fields such as mathematics, finance, industrial engineering, and management science. The primal dual algorithm (PDA), which is a classical approach for tackling a certain class of convex-concave saddle point problems, still has shortcomings such as fixed step size and difficulty in accurately solving certain subproblems. Therefore, designing more efficient inexact algorithms to solve these problems has important practical significance. During this investigation, we introduce an inexact golden ratio primal-dual algorithm based on the absolute error criteria of non-negative summable sequences. We establish the global convergence and the $O(1/N)$ rate of convergence for the proposed inexact algorithm, and the effectiveness of the proposed algorithm is verified by the image restoration experiment.} }
Endnote
%0 Conference Paper %T An Inexact Golden Ratio Primal-Dual Algorithm for a Saddle Point Problem %A Jinxiu Liu %A Changjie Fang %A Jingtao Qiu %B Proceedings of 2025 2nd International Conference on Machine Learning and Intelligent Computing %C Proceedings of Machine Learning Research %D 2025 %E Nianyin Zeng %E Ram Bilas Pachori %E Dongshu Wang %F pmlr-v278-liu25e %I PMLR %P 427--433 %U https://proceedings.mlr.press/v278/liu25e.html %V 278 %X Convex optimization problems have wide applications in many fields such as mathematics, finance, industrial engineering, and management science. The primal dual algorithm (PDA), which is a classical approach for tackling a certain class of convex-concave saddle point problems, still has shortcomings such as fixed step size and difficulty in accurately solving certain subproblems. Therefore, designing more efficient inexact algorithms to solve these problems has important practical significance. During this investigation, we introduce an inexact golden ratio primal-dual algorithm based on the absolute error criteria of non-negative summable sequences. We establish the global convergence and the $O(1/N)$ rate of convergence for the proposed inexact algorithm, and the effectiveness of the proposed algorithm is verified by the image restoration experiment.
APA
Liu, J., Fang, C. & Qiu, J.. (2025). An Inexact Golden Ratio Primal-Dual Algorithm for a Saddle Point Problem. Proceedings of 2025 2nd International Conference on Machine Learning and Intelligent Computing, in Proceedings of Machine Learning Research 278:427-433 Available from https://proceedings.mlr.press/v278/liu25e.html.

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