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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 4, Pages 568–575 (Mi zvmmf479)  

This article is cited in 13 scientific papers (total in 13 papers)

On the convergence of a regularization method for variational inequalities

I. V. Konnov

Kazan State University, ul. Kremlyevskaya 18, Kazan, 420008, Tatarstan, Russia

Abstract: For variational inequalities in a finite-dimensional space, the convergence of a regularization method is examined in the case of a nonmonotone basic mapping. It is shown that a fairly general sufficient condition for the existence of solutions to the original problem also guarantees the convergence and existence of solutions to perturbed problems. Examples of applications to problems on order intervals are presented.

Key words: variational inequalities, regularization method, nonmonotone mappings, coercivity condition, order monotonicity.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:4, 541–547

Bibliographic databases:

UDC: 519.658.4
Received: 07.06.2005

Citation: I. V. Konnov, “On the convergence of a regularization method for variational inequalities”, Zh. Vychisl. Mat. Mat. Fiz., 46:4 (2006), 568–575; Comput. Math. Math. Phys., 46:4 (2006), 541–547

Citation in format AMSBIB
\by I.~V.~Konnov
\paper On the convergence of a~regularization method for variational inequalities
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 4
\pages 568--575
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 4
\pages 541--547

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    This publication is cited in the following articles:
    1. Chen J., Ju X., Koebis E., Liou Y.-Ch., “Tikhonov Type Regularization Methods For Inverse Mixed Variational Inequalities”, Optimization  crossref  isi
    2. D. A. Dyabilkin, I. V. Konnov, “Partial regularization method for nonmonotone variational inequalities”, Comput. Math. Math. Phys., 48:3 (2008), 337–345  mathnet  crossref  mathscinet  zmath  isi
    3. Kien B.T., Yao J.-C., Yen N.D., “On the solution existence of pseudomonotone variational inequalities”, J. Global Optim., 41:1 (2008), 135–145  crossref  mathscinet  zmath  isi  elib  scopus
    4. Konnov I.V., “Regularization method for nonmonotone equilibrium problems”, J. Nonlinear Convex Anal., 10:1 (2009), 93–101  mathscinet  zmath  isi
    5. Dyabilkin D.A., Konnov I.V., “Metod chastichnoi regulyarizatsii dlya obobschennoi pryamo-dvoistvennoi sistemy neravenstv”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 11:1 (2010), 318–325  mathnet  elib
    6. Konnov I.V., Dyabilkin D.A., “Nonmonotone equilibrium problems: coercivity conditions and weak regularization”, J. Global Optim., 49:4 (2011), 575–587  crossref  mathscinet  zmath  isi  elib  scopus
    7. Jiang H., Shanbhag U.V., Meyn S.P., “Learning Equilibria in Constrained Nash-Cournot Games with Misspecified Demand Functions”, 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-Ecc), IEEE, 2011, 1018–1023  crossref  isi  scopus
    8. He Y., “The Tikhonov Regularization Method for Set-Valued Variational Inequalities”, Abstract Appl. Anal., 2012, 172061  crossref  mathscinet  zmath  isi  scopus
    9. Luo X.-p., Yang J., “Regularization and Iterative Methods For Monotone Inverse Variational Inequalities”, Optim. Lett., 8:4 (2014), 1261–1272  crossref  mathscinet  zmath  isi  elib  scopus
    10. Luo X.-p., “Tikhonov Regularization Methods For Inverse Variational Inequalities”, Optim. Lett., 8:3 (2014), 877–887  crossref  mathscinet  zmath  isi  elib  scopus
    11. Li F., He Y., “Solvability of a Perturbed Variational Inequality”, Pac. J. Optim., 10:1, SI (2014), 105–111  mathscinet  zmath  isi
    12. Wang M., “The Existence Results and Tikhonov Regularization Method For Generalized Mixed Variational Inequalities in Banach Spaces”, Anal. Math. Phys., 7:2 (2017), 151–163  crossref  mathscinet  zmath  isi  scopus
    13. Luo X.-p., “Solvability of Some Perturbed Generalized Variational Inequalities in Reflexive Banach Spaces”, J. Funct. space, 2018, 3897495  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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