The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact spheres. Convergence results are proved and computational experience is described and illustrated. The motivating application --- chromosome organization in the human cell nucleus --- is discussed briefly, and some illustrative results are presented.
Technical Report, March, 2012. To appear in SIAM Review, 2013.