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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 1, Pages 27–40 (Mi zvmmf717)  

This article is cited in 12 scientific papers (total in 12 papers)

Regularization methods for solving equilibrium programming problems with coupled constraints

A. S. Antipina, F. P. Vasil'evb

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: Regularization methods (stabilization, residual, and quasi-solution) for solving unstable equilibrium problems are proposed for the case when not only the objective function but also the set determined by coupled inequality constraints are given approximately. The convergence of the proposed methods is investigated, and a regularizing operator is constructed.

Key words: equilibrium programming problems, numerical regularization method, unstable problems.

Full text: PDF file (1644 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:1, 23–36

Bibliographic databases:
UDC: 519.853.6
Received: 24.06.2004

Citation: A. S. Antipin, F. P. Vasil'ev, “Regularization methods for solving equilibrium programming problems with coupled constraints”, Zh. Vychisl. Mat. Mat. Fiz., 45:1 (2005), 27–40; Comput. Math. Math. Phys., 45:1 (2005), 23–36

Citation in format AMSBIB
\Bibitem{AntVas05}
\by A.~S.~Antipin, F.~P.~Vasil'ev
\paper Regularization methods for solving equilibrium programming problems with coupled constraints
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 1
\pages 27--40
\mathnet{http://mi.mathnet.ru/zvmmf717}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2151043}
\zmath{https://zbmath.org/?q=an:1114.90150}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 1
\pages 23--36


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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. F. P. Vasil'ev, A. S. Antipin, “Methods for solving unstable equilibrium programming problems with coupled variables”, Proc. Steklov Inst. Math. (Suppl.), 253, suppl. 1 (2006), S229–S246  mathnet  crossref  mathscinet  zmath  elib
    2. I. P. Ryazantseva, “Regularization methods for certain quasi-variational inequalities with inexactly given data in a Hilbert space”, Comput. Math. Math. Phys., 47:8 (2007), 1232–1242  mathnet  crossref  mathscinet
    3. I. P. Ryazantseva, “First-order methods for certain quasi-variational inequalities in a Hilbert space”, Comput. Math. Math. Phys., 47:2 (2007), 183–190  mathnet  crossref  mathscinet  zmath
    4. Alvarez I., Poznyak A., Malo A., “Urban Traffic Control Problem via a Game Theory Application”, Proceedings of the 46th IEEE Conference on Decision and Control, Vols 1-14, IEEE Conference on Decision and Control - Proceedings, IEEE, 2007, 4979–4983  isi
    5. Ryazantseva I.P., “Second-order methods for some quasivariational inequalities”, Differential Equations, 44:7 (2008), 1006–1017  crossref  mathscinet  zmath  isi  elib  scopus
    6. Alvarez I., Poznyak A., Malo A., “Urban Traffic Control Problem a Game Theory Approach”, 47th IEEE Conference on Decision and Control, 2008 (CDC 2008), IEEE Conference on Decision and Control, IEEE, 2008, 2168–2172  isi
    7. Alvarez I., Poznyak A., “Game Theory Applied to Urban Traffic Control Problem”, International Conference on Control, Automation and Systems (Iccas 2010), IEEE, 2010, 2164–2169  isi
    8. I. P. Ryazantseva, “Certain first-order iterative methods for mixed variational inequalities in a Hilbert space”, Comput. Math. Math. Phys., 51:5 (2011), 713–721  mathnet  crossref  mathscinet  isi
    9. Ryazantseva I.P., “On Continuous First-Order Methods and their Regularized Versions for Mixed Variational Inequalities”, Differ. Equ., 48:7 (2012), 1005–1017  crossref  mathscinet  zmath  isi  elib  elib  scopus
    10. I. P. Ryazantseva, “Iterative processes of the second order monotone inclusions in a Hilbert space”, Russian Math. (Iz. VUZ), 57:7 (2013), 45–52  mathnet  crossref
    11. Vladislav I. Zhukovskiy, Konstantin N. Kudryavtsev, “Pareto-equilibrium strategy profile”, Autom. Remote Control, 77:8 (2016), 1500–1510  mathnet  crossref  isi
    12. Zhukovskiy V.I., Makarkina T.V., Vysokos M.I., “A New Approach to Noncooperative Games Under Uncertainty”, Int. Game Theory Rev., 20:1 (2018), 1750024  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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