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  • 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 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 signif- icantly improves existing results in the domain.
  • 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 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 signif- icantly improves existing results in the domain. (en)
Title
  • Finding largest small polygons with GloptiPoly
  • Finding largest small polygons with GloptiPoly (en)
skos:prefLabel
  • Finding largest small polygons with GloptiPoly
  • Finding largest small polygons with GloptiPoly (en)
skos:notation
  • RIV/68407700:21230/10:00185281!RIV12-MSM-21230___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GAP103/10/0628), Z(MSM6840770038)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
  • Henrion, Didier
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 259207
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21230/10:00185281
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Extremal convex polygons; global optimization; nonconvex quadratic programming; semidefinite programming (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [67B41D41478D]
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Henrion, Didier
  • Messine, F.
http://linked.open...n/vavai/riv/zamer
http://localhost/t...ganizacniJednotka
  • 21230
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