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Zh. Vychisl. Mat. Mat. Fiz., 2004, Volume 44, Number 11, Pages 2001–2019 (Mi zvmmf747)  

This article is cited in 28 scientific papers (total in 28 papers)

A regularized gradient dual method for the inverse problem of a final observation for a parabolic equation

M. I. Sumin

N. I. Lobachevski State University of Nizhni Novgorod, Faculty of Mechanics and Mathematics

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English version:
Computational Mathematics and Mathematical Physics, 2004, 44:11, 1903–1921

Bibliographic databases:
UDC: 519.633.9
MSC: Primary 49N45; Secondary 49M15, 65M32
Received: 08.10.2003
Revised: 11.05.2004

Citation: M. I. Sumin, “A regularized gradient dual method for the inverse problem of a final observation for a parabolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 44:11 (2004), 2001–2019; Comput. Math. Math. Phys., 44:11 (2004), 1903–1921

Citation in format AMSBIB
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\by M.~I.~Sumin
\paper A regularized gradient dual method for the inverse problem of a final observation for a parabolic equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2004
\vol 44
\issue 11
\pages 2001--2019
\mathnet{http://mi.mathnet.ru/zvmmf747}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2129854}
\zmath{https://zbmath.org/?q=an:1121.49038}
\elib{https://elibrary.ru/item.asp?id=13457981}
\transl
\jour Comput. Math. Math. Phys.
\yr 2004
\vol 44
\issue 11
\pages 1903--1921


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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. M. I. Sumin, “Dvoistvennyi regulyarizovannyi algoritm v zadachakh optimizatsii i obratnykh zadachakh”, Izv. IMI UdGU, 2006, no. 3(37), 147–148  mathnet
    2. M. I. Sumin, “Regularized dual method for nonlinear mathematical programming”, Comput. Math. Math. Phys., 47:5 (2007), 760–779  mathnet  crossref  mathscinet
    3. M. I. Sumin, “Duality-based regularization in a linear convex mathematical programming problem”, Comput. Math. Math. Phys., 47:4 (2007), 579–600  mathnet  crossref  mathscinet  zmath  elib  elib
    4. Gaikovich K.P., Sumin M. I, “Dual Regularization in Inverse Problem of Low Frequency Dielectric Profiling”, 2008 4th International Conference on Ultrawideband and Ultrashort Impulse Signals, Proceedings, 2008, 186–188  crossref  isi  scopus
    5. M. I. Sumin, “The first variation and Pontryagin's maximum principle in optimal control for partial differential equations”, Comput. Math. Math. Phys., 49:6 (2009), 958–978  mathnet  crossref  zmath  isi  elib  elib
    6. M. I. Sumin, “Parametric dual regularization for an optimal control problem with pointwise state constraints”, Comput. Math. Math. Phys., 49:12 (2009), 1987–2005  mathnet  crossref  isi
    7. Gaikovich K.P., Kuterin F.A., Smirnov A.I., Sumin M.I., “Dvoistvennaya regulyarizatsiya v obratnoi zadache UNCh-zondirovaniya zemnoi kory”, Vestn. Nizhegorodskogo un-ta im. N. I. Lobachevskogo, 2009, no. 1, 47–52
    8. Sumin M.I., “Parametricheskaya dvoistvennaya regulyarizatsiya v optimizatsii, optimalnom upravlenii i obratnykh zadachakh”, Vestn. Tambovskogo un-ta. Ser.: Estestvennye i tekhnicheskie nauki, 15:1 (2010), 467–492  elib
    9. M. I. Sumin, “Dual regularization and Pontryagin's maximum principle in a problem of optimal boundary control for a parabolic equation with nondifferentiable functionals”, Proc. Steklov Inst. Math. (Suppl.), 275, suppl. 1 (2011), S161–S177  mathnet  crossref  isi  elib
    10. M. I. Sumin, “Regularized parametric Kuhn–Tucker theorem in a Hilbert space”, Comput. Math. Math. Phys., 51:9 (2011), 1489–1509  mathnet  crossref  mathscinet  isi
    11. Kuterin F.A., “Dvoistvennaya regulyarizatsiya v obratnoi zadache finalnogo nablyudeniya dlya parabolicheskogo uravneniya”, Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2011, no. 3-2, 108–114  elib
    12. Kalinin A.V., Sumin M.I., Tyukhtina A.A., “O regulyariziruyuschikh dvoistvennykh algoritmakh v obratnykh zadachakh finalnogo nablyudeniya dlya sistemy uravnenii maksvella v kvazistatsionarnom magnitnom priblizhenii”, Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2011, no. 4-1, 166–172  elib
    13. Sumin M.I., “Parametricheskaya dvoistvennaya regulyarizatsiya i teorema kuna-takkera”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki, 16:1 (2011), 77–89  elib
    14. A. V. Kanatov, M. I. Sumin, “Sequential stable Kuhn–Tucker theorem in nonlinear programming”, Comput. Math. Math. Phys., 53:8 (2013), 1078–1098  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    15. M. I. Sumin, “Ob ustoichivom sekventsialnom printsipe Lagranzha v vypuklom programmirovanii i ego primenenii pri reshenii neustoichivykh zadach”, Tr. IMM UrO RAN, 19, no. 4, 2013, 231–240  mathnet  mathscinet  elib
    16. M. I. Sumin, “Stable sequential convex programming in a Hilbert space and its application for solving unstable problems”, Comput. Math. Math. Phys., 54:1 (2014), 22–44  mathnet  crossref  crossref  isi  elib  elib
    17. Mikhail I. Sumin, “Regularization of Pontryagin maximum principle in optimal control of distributed systems”, Ural Math. J., 2:2 (2016), 72–86  mathnet  crossref  zmath
    18. Kalinin A.V. Sumin M.I. Tyukhtina A.A., “Stable sequential Lagrange principles in the inverse final observation problem for the system of Maxwell equations in the quasistationary magnetic approximation”, Differ. Equ., 52:5 (2016), 587–603  crossref  mathscinet  zmath  isi  elib  scopus
    19. Gaikovich K.P. Gaikovich P.K. Maksimovitch Y.S. Smirnov A.I. Sumin M.I., “Dual regularization in non-linear inverse scattering problems”, Inverse Probl. Sci. Eng., 24:7 (2016), 1215–1239  crossref  mathscinet  zmath  isi  elib  scopus
    20. F. A. Kuterin, M. I. Sumin, “Regulyarizovannyi iteratsionnyi printsip maksimuma Pontryagina v optimalnom upravlenii. II. Optimizatsiya raspredelennoi sistemy”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:1 (2017), 26–41  mathnet  crossref  elib
    21. A. V. Kalinin, M. I. Sumin, A. A. Tyukhtina, “Inverse final observation problems for Maxwell's equations in the quasi-stationary magnetic approximation and stable sequential Lagrange principles for their solving”, Comput. Math. Math. Phys., 57:2 (2017), 189–210  mathnet  crossref  crossref  isi  elib
    22. A. A. Gorshkov, M. I. Sumin, “Regulyarizatsiya printsipa maksimuma Pontryagina v zadache optimalnogo granichnogo upravleniya dlya parabolicheskogo uravneniya s fazovymi ogranicheniyami v lebegovykh prostranstvakh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:2 (2017), 162–177  mathnet  crossref  elib
    23. Sumin M.I., “Regularized Lagrange Principle and Pontryagin Maximum Principle in Optimal Control and Inverse Problems”, IFAC PAPERSONLINE, 51:32 (2018), 871–876  crossref  isi
    24. M. I. Sumin, “Zachem nuzhna regulyarizatsiya printsipa Lagranzha i printsipa maksimuma Pontryagina i chto ona daet”, Vestnik Tambovskogo universiteta. Seriya: estestvennye i tekhnicheskie nauki, 23:124 (2018), 757–775  mathnet  crossref  elib
    25. M. I. Sumin, “Regulyarizovannye printsip Lagranzha i printsip maksimuma Pontryagina v optimalnom upravlenii i obratnykh zadachakh”, Tr. IMM UrO RAN, 25, no. 1, 2019, 279–296  mathnet  crossref  elib
    26. F. A. Kuterin, A. A. Evtushenko, “Ustoichivyi sekventsialnyi printsip maksimuma Pontryagina v zadache optimalnogo upravleniya c fazovymi ogranicheniyami”, Materialy Voronezhskoi zimneimatematicheskoi shkolySovremennye metody teorii funktsiii smezhnye problemy.28 yanvarya–2 fevralya 2019 g.Chast 2, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 171, VINITI RAN, M., 2019, 102–113  mathnet  crossref
    27. M. I. Sumin, “Regulyarizatsiya printsipa maksimuma Pontryagina v vypukloi zadache optimalnogo granichnogo upravleniya dlya parabolicheskogo uravneniya s operatornym ogranicheniem-ravenstvom”, Tr. IMM UrO RAN, 27, no. 2, 2021, 221–237  mathnet  crossref  elib
    28. M. I. Sumin, “Printsip Lagranzha i ego regulyarizatsiya kak teoreticheskaya osnova ustoichivogo resheniya zadach optimalnogo upravleniya i obratnykh zadach”, Vestnik rossiiskikh universitetov. Matematika, 26:134 (2021), 151–171  mathnet  crossref
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