  A small polygon is a polygon of unit diameter. The maximal area of a small
polygon with $n=2m$ vertices is not known when $m\ge 7$. Finding the largest
small $n$-gon for a given number $n\ge 3$ 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 $6 \le n \le 12$, the
algorithm proposed in this work converges to known global optimal solutions
found in the literature.
