Finding largest small polygons with GloptiPoly

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F10%3A00185281" target="_blank" >RIV/68407700:21230/10:00185281 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Finding largest small polygons with GloptiPoly

Popis výsledku v původním jazyce

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 lit- erature, namely for all odd n, and for n = 4; 6 and 8. Thus, for even n 10, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic pro- gramming problems which can challenge state-of-the-art global opti- mization algorithms. We show that a recentlydeveloped 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 signif- icantly improves existing results in the domain.

Název v anglickém jazyce

Finding largest small polygons with GloptiPoly

Popis výsledku anglicky

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 lit- erature, namely for all odd n, and for n = 4; 6 and 8. Thus, for even n 10, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic pro- gramming problems which can challenge state-of-the-art global opti- mization algorithms. We show that a recentlydeveloped 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 signif- icantly improves existing results in the domain.

Druh

O - Ostatní výsledky

CEP obor

BC - Teorie a systémy řízení

OECD FORD obor

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Projekt

<a href="/cs/project/GAP103%2F10%2F0628" target="_blank" >GAP103/10/0628: Semidefinitní programování po nelineární dynamické systémy</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2010

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů