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Two methods for the maximization of homogeneous polynomials over the simplex

Author

Listed:
  • Faizan Ahmed

    (University of Twente)

  • Georg Still

    (University of Twente)

Abstract

The paper deals with the numerical solution of the problem P to maximize a homogeneous polynomial over the unit simplex. We discuss the convergence properties of the so-called replicator dynamics for solving P. We further examine an ascent method, which also makes use of the replicator transformation. Numerical experiments with polynomials of different degrees illustrate the theoretical convergence results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:2:d:10.1007_s10589-021-00307-1
    DOI: 10.1007/s10589-021-00307-1
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    References listed on IDEAS

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    1. Polyxeni-Margarita Kleniati & Panos Parpas & Berç Rustem, 2010. "Partitioning procedure for polynomial optimization," Journal of Global Optimization, Springer, vol. 48(4), pages 549-567, December.
    2. 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.
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    Cited by:

    1. Muhammad Faisal Iqbal & Faizan Ahmed, 2022. "Approximation Hierarchies for the Copositive Tensor Cone and Their Application to the Polynomial Optimization over the Simplex," Mathematics, MDPI, vol. 10(10), pages 1-17, May.

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