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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 5, Pages 781–798 (Mi zvmmf465)  

This article is cited in 4 scientific papers (total in 4 papers)

An extraproximal method for solving equilibrium programming problems in a Hilbert space

A. S. Stukalov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: A regularized method of the proximal type for solving equilibrium problems in a Hilbert space is proposed. The method is combined with an approximation of the original problem. The convergence of the method is analyzed, and a regularizing operator is constructed.

Key words: equilibrium programming, regularization, approximation, extraproximal method, Nash game.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:5, 743–761

Bibliographic databases:

UDC: 519.658.4
Received: 28.11.2005

Citation: A. S. Stukalov, “An extraproximal method for solving equilibrium programming problems in a Hilbert space”, Zh. Vychisl. Mat. Mat. Fiz., 46:5 (2006), 781–798; Comput. Math. Math. Phys., 46:5 (2006), 743–761

Citation in format AMSBIB
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\by A.~S.~Stukalov
\paper An extraproximal method for solving equilibrium programming problems in a~Hilbert space
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 5
\pages 781--798
\mathnet{http://mi.mathnet.ru/zvmmf465}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2286275}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 5
\pages 743--761
\crossref{https://doi.org/10.1134/S0965542506050022}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746046705}


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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. Kumam P., Katchang Ph., “A Viscosity of Extragradient Approximation Method for Finding Equilibrium Problems, Variational Inequalities and Fixed Point Problems for Nonexpansive Mappings”, Nonlinear Anal.-Hybrid Syst., 3:4 (2009), 475–486  crossref  mathscinet  zmath  isi  elib  scopus
    2. Kumam P. Katchang Ph., “A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings”, J. Appl. Math., 2012, 414831  crossref  mathscinet  zmath  isi  scopus
    3. Katchang Ph. Kumam P., “An Iterative Algorithm for Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudo-Contractive Mappings with Optimization Problems”, J. Glob. Optim., 56:4, SI (2013), 1563–1589  crossref  mathscinet  zmath  isi  elib  scopus
    4. Lyashko S.I. Semenov V.V., “A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming”, Optimization and Its Applications in Control and Data Sciences: in Honor of Boris T. Polyak'S 80Th Birthday, Springer Optimization and Its Applications, 115, ed. Goldengorin B., Springer International Publishing Ag, 2016, 315–325  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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