Locating Objects in the Plane Using Global Optimization Techniques

We address the problem of locating objects in the plane such as segments, arcs of circumferences, arbitrary convex sets, their complements or their boundaries. Given a set of points, we seek the rotation and translation for such an object optimizing a very general performance measure, which includes as a particular case the classical objectives in semi-obnoxious facility location. In general, the above-mentioned model yields a global optimization problem, whose resolution is dealt with using difference of convex (DC) techniques such as outer approximation or branch and bound.