Modified limited-memory BFGS method with a cautious update for generalized semi-symmetric tensor equations

Yuncheng Xu; Sanyang Liu; Huiping Cao; Yuncheng Xu; Sanyang Liu; Huiping Cao

doi:10.3934/jimo.2026172

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 10: 4978-5000. doi: 10.3934/jimo.2026172

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Research article

Modified limited-memory BFGS method with a cautious update for generalized semi-symmetric tensor equations

1.
School of mathematics and statistics, Xidian University, Xi'an, Shaanxi, China
2.
School of sciences, Xi'an Polytechnic University, Xi'an, Shaanxi, China

Received: 07 July 2026 Revised: 01 September 2026 Accepted: 07 September 2026 Published: 11 September 2026
90C30, 90C26

For the generalized semi-symmetric tensor equations, this paper reformulates the equations as a nonlinear least-squares problem and proposes a modified L-BFGS method with a cautious update. The method constructs a candidate modified curvature vector using high-order curvature information and employs a cautious criterion to select reliable curvature pairs. Under suitable assumptions, the global convergence of the proposed method is established with a Wolfe line search. Numerical experiments on semi-symmetric tensor test problems with positive and nonuniform coupling show that the proposed method exhibits good stability and competitive performance.
- generalized tensor equations,
- semi-symmetric tensors,
- limited-memory BFGS method,
- cautious update,
- global convergence
Citation: Yuncheng Xu, Sanyang Liu, Huiping Cao. Modified limited-memory BFGS method with a cautious update for generalized semi-symmetric tensor equations[J]. Journal of Industrial and Management Optimization, 2026, 22(10): 4978-5000. doi: 10.3934/jimo.2026172

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Abstract

For the generalized semi-symmetric tensor equations, this paper reformulates the equations as a nonlinear least-squares problem and proposes a modified L-BFGS method with a cautious update. The method constructs a candidate modified curvature vector using high-order curvature information and employs a cautious criterion to select reliable curvature pairs. Under suitable assumptions, the global convergence of the proposed method is established with a Wolfe line search. Numerical experiments on semi-symmetric tensor test problems with positive and nonuniform coupling show that the proposed method exhibits good stability and competitive performance.

References

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