Finding largest small polygons with GloptiPoly

Kód výsledku v 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>

Výsledek na webu

<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>

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 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

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 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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

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

2013

Kód důvěrnosti údajů

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

Název periodika

Journal of Global Optimization

ISSN

0925-5001

e-ISSN

—

Svazek periodika

56

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

12

Strana od-do

1017-1028

Kód UT WoS článku

000321260700016

EID výsledku v databázi Scopus

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