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Saddle points of rational functions

Author

Listed:
  • Guangming Zhou

    (Xiangtan University)

  • Qin Wang

    (Xiangtan University)

  • Wenjie Zhao

    (Xiangtan University)

Abstract

This paper concerns saddle points of rational functions, under general constraints. Based on optimality conditions, we propose an algorithm for computing saddle points. It uses Lasserre’s hierarchy of semidefinite relaxation. The algorithm can get a saddle point if it exists, or it can detect its nonexistence if it does not. Numerical experiments show that the algorithm is efficient for computing saddle points of rational functions.

Suggested Citation

  • Guangming Zhou & Qin Wang & Wenjie Zhao, 2020. "Saddle points of rational functions," Computational Optimization and Applications, Springer, vol. 75(3), pages 817-832, April.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:3:d:10.1007_s10589-019-00141-6
    DOI: 10.1007/s10589-019-00141-6
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    References listed on IDEAS

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    1. Jibetean, D. & de Klerk, E., 2006. "Global optimization of rational functions : A semidefinite programming approach," Other publications TiSEM 25febbc3-cd0c-4eb7-9d37-d, Tilburg University, School of Economics and Management.
    2. Feng Guo & Li Wang & Guangming Zhou, 2014. "Minimizing rational functions by exact Jacobian SDP relaxation applicable to finite singularities," Journal of Global Optimization, Springer, vol. 58(2), pages 261-284, February.
    3. Bruce Cox & Anatoli Juditsky & Arkadi Nemirovski, 2017. "Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 402-435, February.
    4. A. Nedić & A. Ozdaglar, 2009. "Subgradient Methods for Saddle-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 205-228, July.
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    Cited by:

    1. Wenjie Zhao & Guangming Zhou, 2022. "Local saddle points for unconstrained polynomial optimization," Computational Optimization and Applications, Springer, vol. 82(1), pages 89-106, May.

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