A Linearized Alternating Direction Method of Multipliers for Solving Complex Semi-Symmetric Tensor Equations and its Applications

Shenghao Feng (), Yimin Wei (), Renjie Xu () and Eric King-wah Chu ()
Additional contact information
Shenghao Feng: Fudan University
Yimin Wei: Fudan University
Renjie Xu: Hong Kong Science Park
Eric King-wah Chu: Monash University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 930-959

Abstract: Abstract In this study, we consider the complex tensor equation. We propose a linearized alternating direction method of multipliers (LADMM) through the Wirtinger calculus technique. Compared to the alternating direction method of multipliers (ADMM), our LADMM algorithm is more robust and does not need to solve the linear equation in each iteration. By applying the tensor-train (TT) decomposition, we only need to compute matrix products and third-order tensor products instead of high-order tensor products. Under mild assumptions, we prove that all limit points of the sequences generated by our LADMM algorithm satisfy the corresponding Karush-Kuhn-Tucker (KKT) conditions, and the residuals of the sequences converge to 0. Moreover, we solve US-eigenvalue problems, higher-order Markov chain problems, and general constrained tensor equations by using our LADMM algorithm. Finally, we conduct some numerical experiments to illustrate the effectiveness of our LADMM algorithm.

Keywords: Complex tensor equation; complex tensor least squares problem; LADMM; Wirtinger calculus; KKT conditions; TT-decomposition; 15A18; 15A69; 65F10; 65F15 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-025-00812-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:indpam:v:56:y:2025:i:3:d:10.1007_s13226-025-00812-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-025-00812-7

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().