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

Faizan Ahmed; Georg Still

doi:10.1007/s10957-019-01498-8

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 journal › Article › Academic › peer-review

4 Citations (Scopus)

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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 language	English
Pages (from-to)	972-996
Number of pages	25
Journal	Journal of optimization theory and applications
Volume	181
Issue number	3
DOIs	https://doi.org/10.1007/s10957-019-01498-8
Publication status	Published - 1 Jun 2019

Keywords

Evolutionarily stable strategies
Genericity properties
Homogeneous polynomials
Optimization over the simplex
Stability of maximizers
22/4 OA procedure

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10.1007/s10957-019-01498-8

Ahmed-2019-Maximization-of-homogeneous-polynomFinal published version, 460 KBLicence: Taverne

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KW - Genericity properties

KW - Homogeneous polynomials

KW - Optimization over the simplex

KW - Stability of maximizers

KW - 22/4 OA procedure

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

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Keywords

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