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Description
  • We consider the problem of minimizing a functional (such as the area, perimeter and surface) within the class of convex bodies whose support functions are trigonometric polynomials. The convexity constraint is transformed via the Fejér-Riesz theorem on positive trigonometric polynomials into a semidefinite programming problem. Several problems such as the minimization of the area in the class of constantwidth planar bodies, rotors and space bodies of revolution are revisited. The approach seems promising to investigate more difficult optimization problems in the class of three-dimensional convex bodies.
  • We consider the problem of minimizing a functional (such as the area, perimeter and surface) within the class of convex bodies whose support functions are trigonometric polynomials. The convexity constraint is transformed via the Fejér-Riesz theorem on positive trigonometric polynomials into a semidefinite programming problem. Several problems such as the minimization of the area in the class of constantwidth planar bodies, rotors and space bodies of revolution are revisited. The approach seems promising to investigate more difficult optimization problems in the class of three-dimensional convex bodies. (en)
Title
  • Semidefinite programming for optimizing convex bodies under width constraints
  • Semidefinite programming for optimizing convex bodies under width constraints (en)
skos:prefLabel
  • Semidefinite programming for optimizing convex bodies under width constraints
  • Semidefinite programming for optimizing convex bodies under width constraints (en)
skos:notation
  • RIV/68407700:21230/12:00194284!RIV13-GA0-21230___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GAP103/10/0628)
http://linked.open...iv/cisloPeriodika
  • 6
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
  • 167401
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21230/12:00194284
http://linked.open...riv/jazykVysledku
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  • convexity; optimization; semidefinite programming; support function (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV
  • [00758F18C446]
http://linked.open...i/riv/nazevZdroje
  • Optimization Methods and Software
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  • 27
http://linked.open...iv/tvurceVysledku
  • Henrion, Didier
  • Bayen, T.
http://linked.open...ain/vavai/riv/wos
  • 000306841500009
issn
  • 1055-6788
number of pages
http://bibframe.org/vocab/doi
  • 10.1080/10556788.2010.547580
http://localhost/t...ganizacniJednotka
  • 21230
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