Papers › Largest small polygons: A sequential convex optimization approach
Largest small polygons: A sequential convex optimization approach
Christian Bingane
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A small polygon is a polygon of unit diameter. The maximal area of a small polygon with n=2m vertices is not known when m≥7. Finding the largest small n-gon for a given number n≥3 can be formulated as a nonconvex quadratically constrained quadratic optimization problem. We propose to solve this problem with a sequential convex optimization approach, which is an ascent algorithm guaranteeing convergence to a locally optimal solution. Numerical experiments on polygons with up to n=128 sides suggest that the optimal solutions obtained are near-global. Indeed, for even 6 ≤n ≤12, the algorithm proposed in this work converges to known global optimal solutions found in the literature.
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