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

Faizan Ahmed*, Georg Still

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    1 Citation (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)972-996
    Number of pages25
    JournalJournal of optimization theory and applications
    Volume181
    Issue number3
    DOIs
    Publication statusPublished - 1 Jun 2019

    Keywords

    • Evolutionarily stable strategies
    • Genericity properties
    • Homogeneous polynomials
    • Optimization over the simplex
    • Stability of maximizers

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