G-2020-53
Tight bounds on the maximal perimeter and the maximal width of convex small polygons
BibTeX reference
A small polygon is a polygon of unit diameter. The maximal perimeter and the maximal width of a convex small polygon with n=2s
vertices are not known when s≥4
. In this paper, we construct a family of convex small n
-gons, n=2s
and s≥3
, and show that the perimeters and the widths obtained cannot be improved for large n
by more than a/n6
and b/n4
respectively, for certain positive constants a
and b
. In addition, we formulate the maximal perimeter problem as a nonconvex quadratically constrained quadratic optimization problem and, for n=2s
with 3≤s≤7
, we provide near-global optimal solutions obtained with a sequential convex optimization approach.
Published October 2020 , 18 pages
This cahier was revised in May 2021
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