Abstract
The hexagon and heptagon with unit diameter and maximum sum of Euclidean distances between vertices are determined by enumerating diameter configurations, and by using a branch and cut algorithm for nonconvex quadratic programming. Lower bounds on the value on this sum are presented for polygon with a larger number of vertices.
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Dedicated with thanks to Professor Hoang Tuy, founder of global optimization, on the occasion of his 80th birthday.
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Audet, C., Guillou, A., Hansen, P. et al. The small hexagon and heptagon with maximum sum of distances between vertices. J Glob Optim 49, 467–480 (2011). https://doi.org/10.1007/s10898-010-9572-2
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DOI: https://doi.org/10.1007/s10898-010-9572-2