A Subspace Modified Broyden–Fletcher–Goldfarb–Shanno Method for $$\mathcal {B}$$B-eigenvalues of Symmetric Tensors

Mingyuan Cao (), Qingdao Huang (), Chaoqian Li () and Yueting Yang ()
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Mingyuan Cao: Beihua University
Qingdao Huang: Jilin University
Chaoqian Li: Yunnan University
Yueting Yang: Beihua University

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 2, No 6, 419-432

Abstract: Abstract In this paper, finding the $$\mathcal {B}$$B-eigenvalues of a symmetric tensor is equivalent to solving a least-square optimization problem. Based on the subspace technique, a trust region algorithm is presented. In trust region subproblem, the modified Broyden–Fletcher–Goldfarb–Shanno formula is adopted to generate the approximated matrices. In order to reduce the computation cost in each iteration, the quadratic subproblem is constructed in a subspace with lower dimension. Theoretic analysis of the given algorithm and convergence properties of the optimal solutions are established. Numerical results show that this method is efficient.

Keywords: Symmetric tensors; $$\mathcal {B}$$ B -eigenvalues; Modified Broyden–Fletcher–Goldfarb–Shanno; Subspace technique; Global convergence; 15A18; 15A69; 90C55 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-019-01617-5

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