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Diskretn. Anal. Issled. Oper., 2014, Volume 21, Issue 3, Pages 87–102 (Mi da779)  

This article is cited in 9 scientific papers (total in 9 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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English version:
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
\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
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 3
\pages 400--410

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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  elib
    2. A. Yu. Uteshev, M. V. Yashina, “Metric problems for quadrics in multidimensional space”, J. Symbolic Comput., 68:1 (2015), 287–315  crossref  mathscinet  zmath  isi  elib  scopus
    3. 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  mathnet  crossref  crossref  mathscinet  elib
    4. M. E. Abbasov, “Charged ball method for solving some computational geometry problems”, Vestnik St. Petersburg Univ. Math., 50:3 (2017), 209–216  crossref  crossref  mathscinet  isi  elib  scopus
    5. 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  isi
    6. 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  crossref  isi  scopus
    7. A. Yu. Uteshev, M. V. Goncharova, “Point-to-ellipse and point-to-ellipsoid distance equation analysis”, J. Comput. Appl. Math., 328 (2018), 232–251  crossref  mathscinet  zmath  isi  scopus
    8. 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  mathnet  crossref  crossref  elib
    9. Ch.-Ch. Chou, “A closed-form general solution for the distance of point-to-ellipse in two dimensions”, J. Interdiscip. Math., 22:3 (2019), 337–351  crossref  isi  scopus
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