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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 10, Pages 1768–1777 (Mi zvmmf9762)  

This article is cited in 1 scientific paper (total in 1 paper)

Differential properties of the minimum function for diagonalizable quadratic problems

A. V. Arutyunova, S. E. Zhukovskiya, Z. T. Mingaleevab

a Peoples Friendship University of Russia, Moscow, Russia
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

Abstract: For the problem of minimizing a quadratic functional subject to quadratic equality constraints, the topological and differential properties of the minimum function are examined. It is assumed that all the quadratic forms appearing in the statement of the problem are determined by simultaneously diagonalizable matrices. Under this assumption, sufficient conditions for the minimum function to be Lipschitzian are derived, and a description of the set on which this function may not be differentiable, is given.

Key words: quadratic form, quadratic mapping, minimum function.

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:10, 1342–1350

Bibliographic databases:

UDC: 519.626
Received: 26.03.2011

Citation: A. V. Arutyunov, S. E. Zhukovskiy, Z. T. Mingaleeva, “Differential properties of the minimum function for diagonalizable quadratic problems”, Zh. Vychisl. Mat. Mat. Fiz., 52:10 (2012), 1768–1777; Comput. Math. Math. Phys., 52:10 (2012), 1342–1350

Citation in format AMSBIB
\Bibitem{AruZhuMin12}
\by A.~V.~Arutyunov, S.~E.~Zhukovskiy, Z.~T.~Mingaleeva
\paper Differential properties of the minimum function for diagonalizable quadratic problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2012
\vol 52
\issue 10
\pages 1768--1777
\mathnet{http://mi.mathnet.ru/zvmmf9762}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3150292}
\zmath{https://zbmath.org/?q=an:1274.90219}
\transl
\jour Comput. Math. Math. Phys.
\yr 2012
\vol 52
\issue 10
\pages 1342--1350
\crossref{https://doi.org/10.1134/S0965542512100065}


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    This publication is cited in the following articles:
    1. D. Yu. Karamzin, “The Dines theorem and some other properties of quadratic mappings”, Comput. Math. Math. Phys., 55:10 (2015), 1633–1641  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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