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Packing Ellipsoids with Overlap

Caroline Uhler (caroline.uhler***at***ist.ac.at)
Stephen Wright (swright***at***cs.wisc.edu)

Abstract: 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.

Keywords: Ellipsoid Packing, Semidefinite Programming, Bilevel Optimization, Chromosome Organization

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Applications -- Science and Engineering (Biomedical Applications )

Citation: Technical Report, March, 2012. To appear in SIAM Review, 2013.

Download: [PDF]

Entry Submitted: 04/01/2012
Entry Accepted: 04/01/2012
Entry Last Modified: 02/10/2013

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