Geodesic
Finding the distance between the ellipsoids
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 3, pp. 87-102.

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The problem of finding the nearest points between two ellipsoids is considered. New algorithms for solving this problem were constructed using the theory of exact penalty functions and nonsmooth analysis. We propose two iterative methods of (steepest and hypodifferential) descent. New algorithms (as compared with previously known) have specific advantages, in particular, they are universal and less labor-intensive. The software which implements these algorithms was developed in MATLAB and Maple environment. Bibliogr. 12.
Keywords: nonsmooth analysis, nearest distance, ellipsoid, exact penalty, subdifferential, method of hypodifferential descent. 
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G. Sh. Tamasyan; A. A. Chumakov. Finding the distance between the ellipsoids. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 3, pp. 87-102. http://geodesic.mathdoc.fr/item/DA_2014_21_3_a9/

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