Two methods for the maximization of homogeneous polynomials over the simplex

Faizan Ahmed () and Georg Still ()
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Faizan Ahmed: University of Twente
Georg Still: University of Twente

Computational Optimization and Applications, 2021, vol. 80, issue 2, No 7, 523-548

Abstract: 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.

Keywords: Optimization over the simplex; Homogeneous polynomials; Symmetric tensors; Numerical methods; Replicator transformation; Evolutionarily stable strategies; Convergence properties; 90C26; 91A22; 05C69 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-021-00307-1

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