Proximal Alternating Direction Method of Multipliers with Convex Combination Proximal Centers

Danqing Zhou (), Haiwen Xu and Junfeng Yang ()
Additional contact information
Danqing Zhou: Department of Mathematics, Nanjing University, No. 22, Hankou Road, Gulou District, Nanjing, Jiangsu, P. R. China
Haiwen Xu: School of Science, Civil Aviation Flight University of China, Guanghan, Sichuan, P. R. China
Junfeng Yang: Department of Mathematics, Nanjing University, No. 22, Hankou Road, Gulou District, Nanjing, Jiangsu, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2024, vol. 41, issue 03, 1-28

Abstract: Proximal alternating direction method of multipliers (PADMM) is a classical primal-dual splitting method for solving separable convex optimization problems with linear equality constraints, which have numerous applications in, e.g., signal and image processing, machine learning, and statistics. In this paper, we propose a new variant of PADMM, called PADMC, whose proximal centers are constructed by convex combinations of the iterates. PADMC is able to take advantage of problem structures and preserves the desirable properties of the classical PADMM. We establish iterate convergence as well as ð ’ª(1/K) ergodic and ð ’ª(1/K) nonergodic sublinear convergence rate results measured by function residual and feasibility violation, where K denotes the iteration number. Moreover, we propose two fast variants of PADMC, one achieves faster ð ’ª(1/K2) ergodic convergence rate when one of the component functions is strongly convex, and the other ensures faster ð ’ª(1/K) nonergodic convergence rate measured by constraint violation. Finally, preliminary numerical results on the LASSO and the elastic-net regularization problems are presented to demonstrate the performance of the proposed methods.

Keywords: Separable convex optimization; proximal alternating direction method of multipliers; convex combination; acceleration; ergodic convergence rate (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S021759592350029X
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:apjorx:v:41:y:2024:i:03:n:s021759592350029x

Ordering information: This journal article can be ordered from

DOI: 10.1142/S021759592350029X

Access Statistics for this article

Asia-Pacific Journal of Operational Research (APJOR) is currently edited by Gongyun Zhao

More articles in Asia-Pacific Journal of Operational Research (APJOR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().