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Mat. Zametki, 2013, Volume 94, Issue 1, Pages 36–45 (Mi mz9330)  

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

Abstract: Perturbations of the quadratic form minimization problem under quadratic constraints of the type of equalities are considered. The minimum function $\omega$ 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 $\omega$ 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.

DOI: https://doi.org/10.4213/mzm9330

Full text: PDF file (493 kB)
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English version:
Mathematical Notes, 2013, 94:1, 32–40

Bibliographic databases:

UDC: 517.9
Received: 27.02.2012
Revised: 29.10.2012

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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    This publication is cited in the following articles:
    1. Ganikhodzhaev R. Mukhamedov F. Saburov M., “Elliptic Quadratic Operator Equations”, Acta Appl. Math., 159:1 (2019), 29–74  crossref  mathscinet  isi  scopus
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