Isoperimetric Polygons of Maximum Width |
| |
Authors: | Charles Audet Pierre Hansen Frédéric Messine |
| |
Institution: | 1.GERAD and Département de Mathématiques et de Génie Industriel,école Polytechnique de Montréal,Montréal,Canada;2.GERAD and Département des Méthodes Quantitatives,HEC Montréal,Montréal,Canada;3.école des Hautes études Commerciales,Montréal,Canada;4.ENSEEIHT-IRIT,UMR-CNRS 5505,Toulouse Cedex 7,France |
| |
Abstract: | The value
is shown to be an upper bound on the width of any n-sided polygon with unit perimeter. This bound is reached when n is not a power of 2, and the corresponding optimal solutions are the regular polygons when n is odd and clipped regular Reuleaux polygons when n is even but not a power of 2. Using a global optimization algorithm, we show that the optimal width for the quadrilateral
is
with a precision of 10−4. We propose two mathematical programs to determine the maximum width when n=2
s
with s≥3 and provide approximate, but near-optimal, solutions obtained by various heuristics and local optimization for n=8, 16, and 32.
Work of the first author was supported by NSERC grant 239436-01, AFOSR FA9550-07-1-0302, and ExxonMobil. Work of the second
author was supported by NSERC grant 239436-01. |
| |
Keywords: | Convex polygon Width Perimeter Reuleaux Polygon |
本文献已被 SpringerLink 等数据库收录! |
|