3 research outputs found
Largest small polygons: A sequential convex optimization approach
A small polygon is a polygon of unit diameter. The maximal area of a small
polygon with vertices is not known when . Finding the largest
small -gon for a given number 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 a ascent
algorithm guaranteeing convergence to a locally optimal solution. Numerical
experiments on polygons with up to sides suggest that optimal solutions
obtained are near-global. Indeed, for even , the algorithm
proposed in this work converges to known global optimal solutions found in the
literature