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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, Issue 3, Pages 70–80 (Mi vuu168)  

This article is cited in 6 scientific papers (total in 6 papers)

MATHEMATICS

On singular controls in the sense of the pointwise maximum principle in distributed optimization problems

V. I. Sumin

N. I. Lobachevski State University of Nizhni Novgorod

Abstract: It is proved that for distributed optimization problems a sufficiently typical situation is strong degeneration of the singular controls in the sense of the pointwise maximum principle, when together with the maximum principle (which is a first order necessary optimality condition in the case of spike-shaped variation) a second order necessary optimality conditions also degenerates. A derivation of constructive necessary optimality conditions for singular controls is suggested.

Keywords: distributed optimization problems, guided Volterra functional equations, pointwise maximum principle, singular controls.

Full text: PDF file (228 kB)
References: PDF file   HTML file
UDC: 517.95
MSC: 49K20, 49K22, 49N65, 46A32, 45D05
Received: 01.03.2010

Citation: V. I. Sumin, “On singular controls in the sense of the pointwise maximum principle in distributed optimization problems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 3, 70–80

Citation in format AMSBIB
\Bibitem{Sum10}
\by V.~I.~Sumin
\paper On singular controls in the sense of the pointwise maximum principle in distributed optimization problems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2010
\issue 3
\pages 70--80
\mathnet{http://mi.mathnet.ru/vuu168}
\elib{http://elibrary.ru/item.asp?id=15112951}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. V. Lisachenko, V. I. Sumin, “Printsip maksimuma dlya terminalnoi zadachi optimizatsii sistemy Gursa–Darbu v klasse funktsii s summiruemoi smeshannoi proizvodnoi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 2, 52–67  mathnet  elib
    2. Lisachenko I.V., “Neobkhodimye usloviya optimalnosti dlya terminalnoi zadachi optimizatsii sistemy Gursa-Darbu v klasse funktsii s summiruemoi smeshannoi proizvodnoi”, Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2011, no. 3-2, 115–120  elib
    3. I. V. Lisachenko, V. I. Sumin, “Ob osobykh upravleniyakh printsipa maksimuma dlya terminalnoi zadachi optimizatsii sistemy Gursa–Darbu”, Izv. IMI UdGU, 2012, no. 1(39), 80–81  mathnet
    4. V. I. Sumin, “Osobye optimalnye upravleniya raspredelennykh zadach i volterrovy funktsionalno-operatornye uravneniya”, Izv. IMI UdGU, 2012, no. 1(39), 128–129  mathnet
    5. I. V. Lisachenko, V. I. Sumin, “Ob osobykh upravleniyakh printsipa maksimuma dlya zadachi optimizatsii sistemy Gursa–Darbu”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:4 (2015), 483–491  mathnet  elib
    6. Sumin V.I., “Volterra Functional-Operator Equations in the Theory of Optimal Control of Distributed Systems”, IFAC PAPERSONLINE, 51:32 (2018), 759–764  crossref  isi  scopus
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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