Two methods for the maximization of homogeneous polynomials over the simplex

Faizan Ahmed; Georg Still

doi:10.1007/s10589-021-00307-1

Two methods for the maximization of homogeneous polynomials over the simplex

Faizan Ahmed^*, Georg Still

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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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.

Original language	English
Pages (from-to)	523-548
Number of pages	26
Journal	Computational optimization and applications
Volume	80
Issue number	2
Early online date	5 Aug 2021
DOIs	https://doi.org/10.1007/s10589-021-00307-1
Publication status	Published - Nov 2021

Keywords

Convergence properties
Evolutionarily stable strategies
Homogeneous polynomials
Numerical methods
Optimization over the simplex
Replicator transformation
Symmetric tensors
UT-Hybrid-D

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Ahmed-Still2021_Article_TwoMethodsForTheMaximizationOfFinal published version, 5.05 MBLicence: CC BY

Cite this

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KW - Numerical methods

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KW - Replicator transformation

KW - Symmetric tensors

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Two methods for the maximization of homogeneous polynomials over the simplex

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