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Spherical optimization with complex variablesfor computing US-eigenpairs

Author

Listed:
  • Guyan Ni

    (National University of Defense Technology)

  • Minru Bai

    (Hunan University)

Abstract

The aim of this paper is to compute unitary symmetric eigenpairs (US-eigenpairs) of high-order symmetric complex tensors, which is closely related to the best complex rank-one approximation of a symmetric complex tensor and quantum entanglement. It is also an optimization problem of real-valued functions with complex variables. We study the spherical optimization problem with complex variables including the first-order and the second-order Taylor polynomials, optimization conditions and convex functions of real-valued functions with complex variables. We propose an algorithm and show that it is guaranteed to approximate a US-eigenpair of a symmetric complex tensor. Moreover, if the number of US-eigenpair is finite, then the algorithm is convergent to a US-eigenpair. Numerical examples are presented to demonstrate the effectiveness of the proposed method in finding US-eigenpairs.

Suggested Citation

  • Guyan Ni & Minru Bai, 2016. "Spherical optimization with complex variablesfor computing US-eigenpairs," Computational Optimization and Applications, Springer, vol. 65(3), pages 799-820, December.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:3:d:10.1007_s10589-016-9848-7
    DOI: 10.1007/s10589-016-9848-7
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    References listed on IDEAS

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    1. Chen Ling & Hongjin He & Liqun Qi, 2016. "Higher-degree eigenvalue complementarity problems for tensors," Computational Optimization and Applications, Springer, vol. 64(1), pages 149-176, May.
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    Cited by:

    1. Mengshi Zhang & Xinzhen Zhang & Guyan Ni, 2019. "Calculating Entanglement Eigenvalues for Nonsymmetric Quantum Pure States Based on the Jacobian Semidefinite Programming Relaxation Method," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 787-802, March.
    2. Mengshi Zhang & Guyan Ni & Guofeng Zhang, 2020. "Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement," Computational Optimization and Applications, Springer, vol. 75(3), pages 779-798, April.

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