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Maximization of Homogeneous Polynomials over the Simplex and the Sphere: Structure, Stability, and Generic Behavior

Author

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  • Faizan Ahmed

    (Institute of Space Technology)

  • Georg Still

    (University of Twente)

Abstract

The paper deals with the problem of maximizing a (nonconvex) homogeneous polynomial over the unit simplex. This program is directly related to the concept of evolutionarily stable strategies in biology. Optimality conditions are studied together with related stability properties. It is shown that generically any local maximizer is an evolutionarily stable strategy. We further extend these results to the case of polynomial optimization over the sphere.

Suggested Citation

  • Faizan Ahmed & Georg Still, 2019. "Maximization of Homogeneous Polynomials over the Simplex and the Sphere: Structure, Stability, and Generic Behavior," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 972-996, June.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01498-8
    DOI: 10.1007/s10957-019-01498-8
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    References listed on IDEAS

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    1. Maciej Bukowski & Jacek Miekisz, 2004. "Evolutionary and asymptotic stability in symmetric multi-player games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 41-54, January.
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    Cited by:

    1. Faizan Ahmed & Georg Still, 2021. "Two methods for the maximization of homogeneous polynomials over the simplex," Computational Optimization and Applications, Springer, vol. 80(2), pages 523-548, November.
    2. Roland Hildebrand, 2022. "Semi-definite Representations for Sets of Cubics on the Two-dimensional Sphere," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 666-675, November.

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