Journal of the Operations Research Society of China ›› 2021, Vol. 9 ›› Issue (4): 797-817.doi: 10.1007/s40305-020-00337-2

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  • 收稿日期:2019-11-01 修回日期:2020-04-14 出版日期:2021-12-30 发布日期:2021-11-25
  • 基金资助:
    This work was supported by the National Natural Science Foundation of China (Nos. 11101028 and 11271206), National Key R&D Program of China (No. 2017YFF0207401), and the Fundamental Research Funds for the Central Universities (No.FRF-DF-19-004).

A Levenberg–Marquardt Method for Solving the Tensor Split Feasibility Problem

Yu-Xuan Jin, Jin-Ling Zhao   

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
  • Received:2019-11-01 Revised:2020-04-14 Online:2021-12-30 Published:2021-11-25
  • Contact: Jin-Ling Zhao, Yu-Xuan Jin E-mail:jlzhao@ustb.edu.cn;782181914@qq.com

Abstract: This paper considers the tensor split feasibility problem. Let C and Q be non-empty closed convex set and $\mathcal{A}$ be a semi-symmetric tensor. The tensor split feasibility problem is to find xC such that $\mathcal{A} x^{m-1} \in Q$. If we simply take this problem as a special case of the nonlinear split feasibility problem, then we can directly get a projection method to solve it. However, applying this kind of projection method to solve the tensor split feasibility problem is not so efficient. So we propose a Levenberg– Marquardt method to achieve higher efficiency. Theoretical analyses are conducted, and some preliminary numerical results show that the Levenberg–Marquardt method has advantage over the common projection method.

Key words: Tensor, Split feasibility problem, Semi-symmetric, Projection, Levenberg–Marquardt method

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