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 Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 1, Pages 37–49 (Mi zvmmf10815)

Gradient projection method for optimization problems with a constraint in the form of the intersection of a smooth surface and a convex closed set

Yu. A. Chernyaev

Kazan National Research Technical University, Kazan, 420111 Tatarstan, Russia

Abstract: The gradient projection method is generalized to the case of nonconvex sets of constraints representing the set-theoretic intersection of a smooth surface with a convex closed set. Necessary optimality conditions are studied, and the convergence of the method is analyzed.

Key words: smooth surface, convex closed set, gradient projection method, necessary conditions for a local minimum, convergence of an algorithm.

DOI: https://doi.org/10.1134/S0044466919010058

English version:
Computational Mathematics and Mathematical Physics, 2019, 59:1, 34–45

Bibliographic databases:

UDC: 519.658

Citation: Yu. A. Chernyaev, “Gradient projection method for optimization problems with a constraint in the form of the intersection of a smooth surface and a convex closed set”, Zh. Vychisl. Mat. Mat. Fiz., 59:1 (2019), 37–49; Comput. Math. Math. Phys., 59:1 (2019), 34–45

Citation in format AMSBIB
\Bibitem{Che19} \by Yu.~A.~Chernyaev \paper Gradient projection method for optimization problems with a constraint in the form of the intersection of a smooth surface and a convex closed set \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2019 \vol 59 \issue 1 \pages 37--49 \mathnet{http://mi.mathnet.ru/zvmmf10815} \crossref{https://doi.org/10.1134/S0044466919010058} \elib{https://elibrary.ru/item.asp?id=36954030} \transl \jour Comput. Math. Math. Phys. \yr 2019 \vol 59 \issue 1 \pages 34--45 \crossref{https://doi.org/10.1134/S0965542519010056} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000468086500003} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85065708448} 

• http://mi.mathnet.ru/eng/zvmmf10815
• http://mi.mathnet.ru/eng/zvmmf/v59/i1/p37

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