Journal
SIAM REVIEW
Volume 55, Issue 4, Pages 671-706Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120872309
Keywords
ellipsoid packing; trust-region algorithm; semidefinite programming; chromosome territories
Categories
Funding
- NSF [DMS-0914524, DMS-0906818, DMS-1216318]
- DOE [DE-SC0002283]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1216318, 0914524] Funding Source: National Science Foundation
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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.
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