Finding largest small polygons with GloptiPoly

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F13%3A00186545" target="_blank" >RIV/68407700:21230/13:00186545 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10898-011-9818-7" target="_blank" >http://dx.doi.org/10.1007/s10898-011-9818-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10898-011-9818-7" target="_blank" >10.1007/s10898-011-9818-7</a>

Result language
angličtina
Original language name
Finding largest small polygons with GloptiPoly
Original language description
A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices n. Many instances are already solved in the literature, namely for all odd n, and for n = 4, 6 and 8. Thus, for even n a parts per thousand yen 10, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic programming problems which can challenge state-of-the-art global optimization algorithms. We show that a recently developed technique for global polynomial optimization, based on a semidefinite programming approach to the generalized problem of moments and implemented in the public-domain Matlab package GloptiPoly, can successfully find largest small polygons for n = 10 and n = 12. Therefore this significantly improves existing results in the domain. When coupled with accurate convex conic solvers, GloptiPoly can provide numerical guarantees of global optimality, as well as rigor
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GAP103%2F10%2F0628" target="_blank" >GAP103/10/0628: Semidefinite programming for nonlinear dynamical systems</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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