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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 1, Pages 21–33 (Mi zvmmf343)  

This article is cited in 7 scientific papers (total in 7 papers)

A regularized Newton method for solving equilibrium programming problems with an inexactly specified set

A. S. Antipina, F. P. Vasil'evb, A. S. Stukalovb

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: Unstable equilibrium problems are examined in which the objective function and the set where the equilibrium point is sought are specified inexactly. A regularized Newton method, combined with penalty functions, is proposed for solving such problems, and its convergence is analyzed. A regularizing operator is constructed.

Key words: equilibrium programming, regularization, Newton method, penalty functions.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:1, 19–31

Bibliographic databases:

UDC: 519.853
Received: 12.05.2006

Citation: A. S. Antipin, F. P. Vasil'ev, A. S. Stukalov, “A regularized Newton method for solving equilibrium programming problems with an inexactly specified set”, Zh. Vychisl. Mat. Mat. Fiz., 47:1 (2007), 21–33; Comput. Math. Math. Phys., 47:1 (2007), 19–31

Citation in format AMSBIB
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\by A.~S.~Antipin, F.~P.~Vasil'ev, A.~S.~Stukalov
\paper A~regularized Newton method for solving equilibrium programming problems with an inexactly specified set
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 1
\pages 21--33
\mathnet{http://mi.mathnet.ru/zvmmf343}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2347924}
\zmath{https://zbmath.org/?q=an:05200958}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 1
\pages 19--31
\crossref{https://doi.org/10.1134/S0965542507010046}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33947522520}


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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. Iusem A.N., Nasri M., “Augmented Lagrangian methods for variational inequality problems”, RAIRO Oper. Res., 44:1 (2010), 5–25  crossref  mathscinet  zmath  isi  scopus
    3. Mashreghi J., Nasri M., “A proximal augmented Lagrangian method for equilibrium problems”, Appl. Anal., 91:1 (2012), 157–172  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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 (2012), 414831, 35 pp.  crossref  mathscinet  zmath  isi  scopus
    5. Mashreghi J., Nasri M., “Hybrid Lagrange multiplier approaches for solving infinite dimensional equilibrium problems with cone constraints”, J. Nonlinear Convex Anal., 13:2 (2012), 331–349  mathscinet  zmath  isi  elib
    6. 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
    7. V. I. Zabotin, Yu. A. Chernyaev, “Newton's method for minimizing a convex twice differentiable function on a preconvex set”, Comput. Math. Math. Phys., 58:3 (2018), 322–327  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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