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Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization

Author

Listed:
  • Naohiko Arima

    (Tokyo Institute of Technology)

  • Sunyoung Kim

    (Ewha W. University)

  • Masakazu Kojima

    (Chuo University)

Abstract

We propose the moment cone relaxation for a class of polynomial optimization problems to extend the results on the completely positive cone programming relaxation for the quadratic optimization model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the polynomial optimization problems, so that efficient numerical methods can be developed in the future. We establish the equivalence between the optimal value of the polynomial optimization problem and that of the moment cone relaxation under conditions similar to the ones assumed in the quadratic optimization model.

Suggested Citation

  • Naohiko Arima & Sunyoung Kim & Masakazu Kojima, 2016. "Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 884-900, March.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:3:d:10.1007_s10957-015-0794-9
    DOI: 10.1007/s10957-015-0794-9
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    Cited by:

    1. Xiaolong Kuang & Luis F. Zuluaga, 2018. "Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization," Journal of Global Optimization, Springer, vol. 70(3), pages 551-577, March.
    2. E. Alper Yıldırım, 2022. "An alternative perspective on copositive and convex relaxations of nonconvex quadratic programs," Journal of Global Optimization, Springer, vol. 82(1), pages 1-20, January.

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