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A semidefinite relaxation method for second-order cone polynomial complementarity problems

Author

Listed:
  • Lulu Cheng

    (Tianjin University)

  • Xinzhen Zhang

    (Tianjin University)

Abstract

This paper discusses how to compute all real solutions of the second-order cone tensor complementarity problem when there are finitely many ones. For this goal, we first formulate the second-order cone tensor complementarity problem as two polynomial optimization problems. Based on the reformulation, a semidefinite relaxation method is proposed by solving a finite number of semidefinite relaxations with some assumptions. Numerical experiments are given to show the efficiency of the method.

Suggested Citation

  • Lulu Cheng & Xinzhen Zhang, 2020. "A semidefinite relaxation method for second-order cone polynomial complementarity problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 629-647, April.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:3:d:10.1007_s10589-019-00162-1
    DOI: 10.1007/s10589-019-00162-1
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    References listed on IDEAS

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    1. Jiawang Nie & Xinzhen Zhang, 2018. "Real eigenvalues of nonsymmetric tensors," Computational Optimization and Applications, Springer, vol. 70(1), pages 1-32, May.
    2. Zheng-Hai Huang & Liqun Qi, 2019. "Tensor Complementarity Problems—Part III: Applications," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 771-791, December.
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