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

Author

Listed:
  • Mingyuan Cao

    (Beihua University)

  • Qingdao Huang

    (Jilin University)

  • Chaoqian Li

    (Yunnan University)

  • Yueting Yang

    (Beihua University)

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.

Suggested Citation

  • Mingyuan Cao & Qingdao Huang & Chaoqian Li & Yueting Yang, 2020. "A Subspace Modified Broyden–Fletcher–Goldfarb–Shanno Method for $$\mathcal {B}$$B-eigenvalues of Symmetric Tensors," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 419-432, February.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:2:d:10.1007_s10957-019-01617-5
    DOI: 10.1007/s10957-019-01617-5
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    References listed on IDEAS

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    1. Chengxian Xu & Jianzhong Zhang, 2001. "A Survey of Quasi-Newton Equations and Quasi-Newton Methods for Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 213-234, March.
    2. Qin Ni & Liqun Qi, 2015. "A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map," Journal of Global Optimization, Springer, vol. 61(4), pages 627-641, April.
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