Convergence Analysis on A Data-Driven Inexact Proximal-Indefinite Stochastic ADMM

Jianchao Bai (), Yang Chen (), Xingju Cai and Xue Yu
Additional contact information
Jianchao Bai: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, P. R. China
Yang Chen: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, P. R. China
Xingju Cai: School of Mathematical Sciences, Ministry of Education Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023, P. R. China
Xue Yu: Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, P. R. China4Beijing Advanced Innovation Center for Future, Blockchain and Privacy Computing, Beijing 100191, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2025, vol. 42, issue 05, 1-30

Abstract: In this paper, we propose an Inexact Proximal-indefinite Stochastic ADMM (abbreviated as IPS-ADMM) to solve a class of separable convex optimization problems whose objective functions consist of two parts: one is an average of many smooth convex functions and the other is a convex but potentially nonsmooth function. The involved smooth subproblem is tackled by an inexact accelerated stochastic gradient method based on an adaptive expansion step to avoid the scenario that the sample size can be extremely huge so that computing the objective function value or its gradient is much more expensive. The involved nonsmooth subproblem is solved inexactly under a relative error criterion to avoid the case that the proximal operator is potentially unavailable. In contrast to most deterministic and stochastic ADMM algorithms, our dual variable updates twice and allows a more flexible and larger stepsize region. By a variational analysis, we characterize the generated iterates as a variational inequality and finally establish the sublinear convergence rate of this IPS-ADMM in terms of the objective function gap and constraint violation. Experiments on solving the 3D CT reconstruction problem in medical imaging and the graph-guided fused lasso problem in machine learning show that our IPS-ADMM is very promising.

Keywords: Convex optimization; stochastic ADMM; proximal-indefinite term; larger stepsize; convergence complexity; machine learning (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0217595925500101
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:42:y:2025:i:05:n:s0217595925500101

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0217595925500101

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 ().