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Unconstrained minimization of block-circulant polynomials via semidefinite program in third-order tensor space

Author

Listed:
  • Meng-Meng Zheng

    (National University of Defense Technology)

  • Zheng-Hai Huang

    (Tianjin University)

  • Sheng-Long Hu

    (Hangzhou Dianzi University)

Abstract

In this paper, unconstrained minimization with block-circulant structured polynomials is studied. A specifically designed method is presented to show that it can solve problems with sizes much larger than the classical Lasserre’s semidefinite relaxation. The proposed approach is in the same spirit of Lasserre’s relaxation but with a careful exploration of the underlying circulant structure, which helps reducing the sizes of the result semidefinite program problems significantly. Despite of the reduction, a certification for the global optimality is derived as well.

Suggested Citation

  • Meng-Meng Zheng & Zheng-Hai Huang & Sheng-Long Hu, 2022. "Unconstrained minimization of block-circulant polynomials via semidefinite program in third-order tensor space," Journal of Global Optimization, Springer, vol. 84(2), pages 415-440, October.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:2:d:10.1007_s10898-022-01148-w
    DOI: 10.1007/s10898-022-01148-w
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    References listed on IDEAS

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