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This article is cited in 8 scientific papers (total in 8 papers)
Finding the distance between the ellipsoids
G. Sh. Tamasyan, A. A. Chumakov
St. Petersburg State University, 35 Universitetskiy Ave.,
198504 Peterhof, St. Petersburg, Russia
Abstract:
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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Journal of Applied and Industrial Mathematics, 2014, 8:3, 400–410
Bibliographic databases:
UDC:
519.85
Received: 02.09.2013
Revised: 11.11.2013
Citation:
G. Sh. Tamasyan, A. A. Chumakov, “Finding the distance between the ellipsoids”, Diskretn. Anal. Issled. Oper., 21:3 (2014), 87–102; J. Appl. Industr. Math., 8:3 (2014), 400–410
Citation in format AMSBIB
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\by G.~Sh.~Tamasyan, A.~A.~Chumakov
\paper Finding the distance between the ellipsoids
\jour Diskretn. Anal. Issled. Oper.
\yr 2014
\vol 21
\issue 3
\pages 87--102
\mathnet{http://mi.mathnet.ru/da779}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3242585}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 3
\pages 400--410
\crossref{https://doi.org/10.1134/S1990478914030132}
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http://mi.mathnet.ru/eng/da779 http://mi.mathnet.ru/eng/da/v21/i3/p87
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M. V. Dolgopolik, G. Sh. Tamasyan, “Ob ekvivalentnosti metodov naiskoreishego i gipodifferentsialnogo spuskov v nekotorykh zadachakh uslovnoi optimizatsii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(2) (2014), 532–542
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A. Yu. Uteshev, M. V. Yashina, “Metric problems for quadrics in multidimensional space”, J. Symbolic Comput., 68:1 (2015), 287–315
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G. Sh. Tamasyan, E. V. Prosolupov, T. A. Angelov, “Comparative study of two fast algorithms for projecting a point to the standard simplex”, J. Appl. Industr. Math., 10:2 (2016), 288–301
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M. E. Abbasov, “Charged ball method for solving some computational geometry problems”, Vestnik St. Petersburg Univ. Math., 50:3 (2017), 209–216
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S. Myshkov, “On the minimax approach in a singularly perturbed control problem”, 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V. F. Demyanov) (CNSA), ed. L. Polyakova, IEEE, 2017, 222–225
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A. Plyushch, P. Lamberti, G. Spinelli, J. Macutkevic, P. Kuzhir, “Numerical simulation of the percolation threshold in non-overlapping ellipsoid composites: toward bottom-up approach for carbon based electromagnetic components realization”, Appl. Sci.-Basel, 8:6 (2018), 882
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A. Yu. Uteshev, M. V. Goncharova, “Point-to-ellipse and point-to-ellipsoid distance equation analysis”, J. Comput. Appl. Math., 328 (2018), 232–251
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E. V. Prosolupov, G. Sh. Tamasyan, “Complexity estimation for an algorithm of searching for zero of a piecewise linear convex function”, J. Appl. Industr. Math., 12:2 (2018), 325–333
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