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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 9, Pages 1616–1629 (Mi zvmmf9539)  

This article is cited in 17 scientific papers (total in 17 papers)

On the convergence of the conditional gradient method in distributed optimization problems

A. V. Chernov

Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950 Russia

Abstract: A theorem is stated on sufficient conditions for the convergence of the conditional gradient method as applied to the optimization of a nonlinear controlled functional–operator equation in a Banach ideal space. The theory is illustrated by application to the controlled Goursat–Darboux problem.

Key words: nonlinear controlled functional–operator equation, optimization problems, conditional gradient method, sufficient conditions for convergence.

Full text: PDF file (1150 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:9, 1510–1523

Bibliographic databases:

UDC: 519.626
Received: 19.01.2011

Citation: A. V. Chernov, “On the convergence of the conditional gradient method in distributed optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 51:9 (2011), 1616–1629; Comput. Math. Math. Phys., 51:9 (2011), 1510–1523

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. Chernov, “Sufficient conditions for the controllability of nonlinear distributed systems”, Comput. Math. Math. Phys., 52:8 (2012), 1115–1127  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    2. Chernov A.V., “O neotritsatelnosti resheniya pervoi kraevoi zadachi dlya parabolicheskogo uravneniya”, Vestn. Nizhegorodskogo un-ta im. N. I. Lobachevskogo, 2012, no. 5-1, 167–170  elib
    3. A. V. Chernov, “Ob $\varepsilon$-ravnovesii v beskoalitsionnykh funktsionalno-operatornykh igrakh so mnogimi uchastnikami”, Tr. IMM UrO RAN, 19, no. 1, 2013, 316–328  mathnet  mathscinet  elib
    4. A. V. Chernov, “Ob upravlyaemosti nelineinykh raspredelennykh sistem na mnozhestve konechnomernykh approksimatsii upravleniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 1, 83–98  mathnet
    5. Andrei V. Chernov, “Ob odnom podkhode k postroeniyu $\varepsilon$-ravnovesiya v beskoalitsionnykh igrakh, svyazannykh s uravneniyami matematicheskoi fiziki, upravlyaemykh mnogimi igrokami”, MTIP, 5:1 (2013), 104–123  mathnet
    6. A. V. Chernov, “Smooth finite-dimensional approximations of distributed optimization problems via control discretization”, Comput. Math. Math. Phys., 53:12 (2013), 1839–1852  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. Chernov A.V., “O nekotorykh svoistvakh skhodimosti v banakhovykh idealnykh prostranstvakh”, Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2013, no. 2-1, 138–141  elib
    8. Chernov A.V., “Ob analoge obobschennogo neravenstva Geldera v prostranstvakh Orlicha”, Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2013, no. 6-1, 157–161  elib
    9. A. V. Chernov, “O gladkosti approksimirovannoi zadachi optimizatsii sistemy Gursa–Darbu na variruemoi oblasti”, Tr. IMM UrO RAN, 20, no. 1, 2014, 305–321  mathnet  mathscinet  elib
    10. A. V. Chernov, “O primenimosti tekhniki parametrizatsii upravleniya k resheniyu raspredelennykh zadach optimizatsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 1, 102–117  mathnet
    11. Chernov A.V., “On the Convexity of Reachability Sets of Controlled Initial-Boundary Value Problems”, Differ. Equ., 50:5 (2014), 700–710  crossref  mathscinet  zmath  isi  elib  scopus
    12. A. V. Chernov, “On the convergence of the conditional gradient method as applied to the optimization of an elliptic equation”, Comput. Math. Math. Phys., 55:2 (2015), 212–226  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    13. A. V. Chernov, “O totalno globalnoi razreshimosti upravlyaemogo uravneniya tipa Gammershteina s variruemym lineinym operatorom”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:2 (2015), 230–243  mathnet  elib
    14. A. V. Chernov, “Ob analoge teoremy Uintnera dlya upravlyaemogo ellipticheskogo uravneniya”, Izv. IMI UdGU, 2015, no. 2(46), 228–235  mathnet  elib
    15. Chernov A.V., “On a Majorant-Minorant Criterion For the Total Preservation of Global Solvability of Distributed Controlled Systems”, Differ. Equ., 52:1 (2016), 111–121  crossref  mathscinet  zmath  isi  elib  scopus
    16. 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
    17. V. I. Sumin, “Upravlyaemye volterrovy funktsionalnye uravneniya i printsip szhimayuschikh otobrazhenii”, Tr. IMM UrO RAN, 25, no. 1, 2019, 262–278  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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