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Local saddle points for unconstrained polynomial optimization

Author

Listed:
  • Wenjie Zhao

    (Xiangtan University)

  • Guangming Zhou

    (Xiangtan University)

Abstract

This paper gives an algorithm for computing local saddle points for unconstrained polynomial optimization. It is based on optimality conditions and Lasserre’s hierarchy of semidefinite relaxations. It can determine the existence of local saddle points. When there are several different local saddle point values, the algorithm can get them from the smallest one to the largest one.

Suggested Citation

  • Wenjie Zhao & Guangming Zhou, 2022. "Local saddle points for unconstrained polynomial optimization," Computational Optimization and Applications, Springer, vol. 82(1), pages 89-106, May.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:1:d:10.1007_s10589-022-00361-3
    DOI: 10.1007/s10589-022-00361-3
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. M.J. Kallio & A. Ruszczynski, 1994. "Perturbation Methods for Saddle Point Computation," Working Papers wp94038, International Institute for Applied Systems Analysis.
    4. Guangming Zhou & Qin Wang & Wenjie Zhao, 2020. "Saddle points of rational functions," Computational Optimization and Applications, Springer, vol. 75(3), pages 817-832, April.
    5. Mamer, J W & Schilling, K E, 1990. "Finite Approximations to a Zero-Sum Game with Incomplete Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 101-106.
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