Newton Algorithm on Constraint Manifolds and the 5-Electron Thomson Problem

Petre Birtea () and Dan Comănescu ()
Additional contact information
Petre Birtea: West University of Timişoara
Dan Comănescu: West University of Timişoara

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 2, No 10, 563-583

Abstract: Abstract We give a description of numerical Newton algorithm on a constraint manifold using only the ambient coordinates (usually Euclidean coordinates) and the geometry of the constraint manifold. We apply the numerical Newton algorithm on a sphere in order to find the critical configurations of the 5-electron Thomson problem. As a result, we find a new critical configuration of a regular pentagonal type. We also make an analytical study of the critical configurations found previously and determine their nature using Morse–Bott theory. The last section contains an analytical study of critical configurations for Riesz s-energy of 5-electron on a sphere, and their bifurcation behavior is pointed out.

Keywords: Newton algorithm; Constraint manifold; Hessian operator; Morse theory; 5-Electron Thomson problem; Riesz s-energy; 49M15; 53-XX (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-016-1049-0 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:173:y:2017:i:2:d:10.1007_s10957-016-1049-0

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

DOI: 10.1007/s10957-016-1049-0

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 ().