Proceedings of TOGO 2010 , pp . 3 – 6 . Optimization problems in planar geometry ∗

Attributes such as perimeter, area, diameter, sum of distances between vertices and width can be evaluated for every planar convex polygon. Fixing one of these attributes while minimizing of maximizing another defines families of optimization problems. Some of these problems have a trivial solution, and several others have been solved, some since the Greeks, by geometrical reasoning. During the last four decades, this geometrical approach has been complemented by global optimization methods. This combination allowed solution of instances than could be solved by any one of these two approaches alone. This talk surveys research on that topic, and proposes directions for further work.