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

Faizan Ahmed () and Georg Still ()
Additional contact information
Faizan Ahmed: Institute of Space Technology
Georg Still: University of Twente

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 3, No 13, 972-996

Abstract: 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.

Keywords: Optimization over the simplex; Homogeneous polynomials; Evolutionarily stable strategies; Stability of maximizers; Genericity properties; 90C26; 90C31; 90C46; 91A22 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-019-01498-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01498-8

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-019-01498-8

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().