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We discuss the convergence properties of the so-called replicator dynamics for solving <jats:italic>P<\/jats:italic>. 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.<\/jats:p>","DOI":"10.1007\/s10589-021-00307-1","type":"journal-article","created":{"date-parts":[[2021,8,5]],"date-time":"2021-08-05T17:03:11Z","timestamp":1628182991000},"page":"523-548","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Two methods for the maximization of homogeneous polynomials over the simplex"],"prefix":"10.1007","volume":"80","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2760-6892","authenticated-orcid":false,"given":"Faizan","family":"Ahmed","sequence":"first","affiliation":[]},{"given":"Georg","family":"Still","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,5]]},"reference":[{"key":"307_CR1","doi-asserted-by":"publisher","first-page":"972","DOI":"10.1007\/s10957-019-01498-8","volume":"181","author":"F Ahmed","year":"2019","unstructured":"Ahmed, F., Still, G.: Maximization of homogeneous polynomials over simplex and sphere: structure, stability, and generic behavior. 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