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Mat. Zametki, 2008, Volume 84, Issue 2, Pages 163–174 (Mi mz4161)  

This article is cited in 11 scientific papers (total in 11 papers)

Nonnegativity of Quadratic Forms on Intersections of Quadrics and Quadratic Maps

A. V. Arutyunov

Peoples Friendship University of Russia

Abstract: The question of the nonnegativity of quadratic forms on intersections of quadratic cones is considered. An answer is given in terms of Lagrange multipliers of the quadratic forms under consideration.

Keywords: quadratic form, quadratic cone, quadratic map, regular zero of a quadratic function, abnormal point, bilinear map, Sard's theorem

DOI: https://doi.org/10.4213/mzm4161

Full text: PDF file (494 kB)
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English version:
Mathematical Notes, 2008, 84:2, 155–165

Bibliographic databases:

UDC: 517.9
Received: 18.10.2007

Citation: A. V. Arutyunov, “Nonnegativity of Quadratic Forms on Intersections of Quadrics and Quadratic Maps”, Mat. Zametki, 84:2 (2008), 163–174; Math. Notes, 84:2 (2008), 155–165

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Arutyunov, “Smooth abnormal problems in extremum theory and analysis”, Russian Math. Surveys, 67:3 (2012), 403–457  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. V. Arutyunov, “Two Problems of the Theory of Quadratic Maps”, Funct. Anal. Appl., 46:3 (2012), 225–227  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. A. V. Arutyunov, S. E. Zhukovskiy, Z. T. Mingaleeva, “Differential properties of the minimum function for diagonalizable quadratic problems”, Comput. Math. Math. Phys., 52:10 (2012), 1342–1350  mathnet  crossref  mathscinet  zmath
    4. Arutyunov A.V., “On two questions of optimization theory concerning quadratic mappings”, Optim. Lett., 6:5 (2012), 1009–1015  crossref  mathscinet  zmath  isi  elib  scopus
    5. A. V. Arutyunov, “Properties of the Minimum Function in the Quadratic Problem”, Math. Notes, 94:1 (2013), 32–40  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. E. R. Avakov, A. V. Arutyunov, D. Yu. Karamzin, “An investigation of smooth maps in a neighbourhood of an abnormal point”, Izv. Math., 78:2 (2014), 213–250  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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
    8. A. V. Arutyunov, S. E. Zhukovskii, “On Surjective Quadratic Mappings”, Math. Notes, 99:2 (2016), 192–195  mathnet  crossref  crossref  mathscinet  isi  elib
    9. A. V. Arutyunov, S. E. Zhukovskiy, “Properties of surjective real quadratic maps”, Sb. Math., 207:9 (2016), 1187–1214  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. A. V. Arutyunov, S. E. Zhukovskiy, D. Yu. Karamzin, “Some properties of two-dimensional surjective $p$-homogeneous maps”, Comput. Math. Math. Phys., 57:7 (2017), 1081–1089  mathnet  crossref  crossref  mathscinet  isi  elib
    11. 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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