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Matematicheskie Zametki, 2013, Volume 94, Issue 1, Pages 36–45
DOI: https://doi.org/10.4213/mzm9330 (Mi mzm9330) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Properties of the Minimum Function in the Quadratic Problem

A. V. Arutyunov

Peoples Friendship University of Russia, Moscow
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DOI: https://doi.org/10.4213/mzm9330
Abstract: Perturbations of the quadratic form minimization problem under quadratic constraints of the type of equalities are considered. The minimum function ω in this problem which, to each perturbation of the original problem, assigns a sharp lower bound in the perturbed problem is studied. Sufficient conditions for the upper and lower semicontinuity of the minimum function ω both at zero and in its neighborhood are obtained. Examples showing the importance of these conditions are given.
Keywords: quadratic mapping, quadratic form minimization, minimum function, upper and lower semicontinuity.
Received: 27.02.2012
Revised: 29.10.2012
English version:
Mathematical Notes, 2013, Volume 94, Issue 1, Pages 32–40
DOI: https://doi.org/10.1134/S0001434613070031
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. V. Arutyunov, “Properties of the Minimum Function in the Quadratic Problem”, Mat. Zametki, 94:1 (2013), 36–45; Math. Notes, 94:1 (2013), 32–40
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm9330
  • https://www.mathnet.ru/eng/mzm/v94/i1/p36
    • This publication is cited in the following 1 articles:
    1. Ganikhodzhaev R. Mukhamedov F. Saburov M., “Elliptic Quadratic Operator Equations”, Acta Appl. Math., 159:1 (2019), 29–74  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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