Uhler, CarolineIST Austria ; Wright, Stephen
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.
This work was supported by NSF grants DMS 0914524, DMS-0906818, and DMS-1216318 and by DOE grant DE-SC0002283.
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Uhler C, Wright S. Packing ellipsoids with overlap. SIAM Review. 2013;55(4):671-706. doi:10.1137/120872309
Uhler, C., & Wright, S. (2013). Packing ellipsoids with overlap. SIAM Review, 55(4), 671–706. https://doi.org/10.1137/120872309
Uhler, Caroline, and Stephen Wright. “Packing Ellipsoids with Overlap.” SIAM Review 55, no. 4 (2013): 671–706. https://doi.org/10.1137/120872309.
C. Uhler and S. Wright, “Packing ellipsoids with overlap,” SIAM Review, vol. 55, no. 4, pp. 671–706, 2013.
Uhler C, Wright S. 2013. Packing ellipsoids with overlap. SIAM Review. 55(4), 671–706.
Uhler, Caroline, and Stephen Wright. “Packing Ellipsoids with Overlap.” SIAM Review, vol. 55, no. 4, Society for Industrial and Applied Mathematics , 2013, pp. 671–706, doi:10.1137/120872309.
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