Abstract
We consider multilinear systems which arise in various applications, such as data mining and numerical differential equations. In this paper, we show that the multilinear system with a nonsingular M-tensor can be formulated equivalently into a geometric programming (GP) problem which can be solved by the barrier-based interior point method with a worst-case polynomial-time complexity. To the best of our knowledge, there is not a complexity analysis for the existing algorithms of the multilinear systems. Numerical results are reported to show the efficiency of the proposed GP method. © 2025 Elsevier Ltd.
| Original language | English |
|---|---|
| Article number | 109462 |
| Journal | Applied Mathematics Letters |
| Volume | 163 |
| Online published | 15 Jan 2025 |
| DOIs | |
| Publication status | Published - Apr 2025 |
Funding
The authors would like to thank the editor and two anonymous referees for their constructive comments which help us to improve the paper. The authors also would like to thank Professor Lixing Han for sharing his code on the Homotopy Method and Professor Hongjin He for the Matlab code on QCA method. This work was supported by Natural Science Foundation of China (12071249), Shandong Provincial Natural Science Foundation (ZR2021JQ01 and ZR2024MA003), Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA) and City University of Hong Kong (Projects 9610034 and 9610460).
Research Keywords
- Complexity
- Interior point algorithm
- Multilinear system
- ℳ-tensor