Optimality conditions for Tucker low-rank tensor optimization

Ziyan Luo () and Liqun Qi ()
Additional contact information
Ziyan Luo: Beijing Jiaotong University
Liqun Qi: 2012 Labs Huawei Technologies Investment Co., Ltd

Computational Optimization and Applications, 2023, vol. 86, issue 3, No 16, 1275-1298

Abstract: Abstract Optimization problems with tensor variables are widely used in statistics, machine learning, pattern recognition, signal processing, computer vision, etc. Among these applications, the low-rankness of tensors is an intrinsic property that can help unearth potential but important structure or feature in the corresponding high-dimensional multi-way datasets, leading to the study on low-rank tensor optimization (LRTO for short). For the general framework of LRTO, little has been addressed in optimization theory. This motivates us to study the optimality conditions, with special emphasis on the Tucker low-rank constrained problems and the Tucker low-rank decomposition-based reformulations. It is noteworthy that all the involved optimization problems are nonconvex, and even discontinuous, due to the complexity of the tensor Tucker rank function or the multi-linear decomposition with the orthogonality or even group sparsity constraints imposed on factor matrices. By employing the tools in variational analysis, especially the normal cones to low-rank matrices and the properties of matrix manifolds, we propose necessary and/or sufficient optimality conditions for Tucker low-rank tensor optimization problems, which will enrich the context of the nonconvex and nonsmooth optimization.

Keywords: Tensor optimization; Optimality conditions; Tucker decomposition; Low-rankness (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-023-00465-4 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:coopap:v:86:y:2023:i:3:d:10.1007_s10589-023-00465-4

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-023-00465-4

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().