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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 12, Pages 1998–2013 (Mi zvmmf207)  

This article is cited in 10 scientific papers (total in 10 papers)

Multicriteria equilibrium programming: Extraproximal methods

A. S. Antipin

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: Multicriteria equilibrium optimization is an efficient tool for mathematical modeling of various situations in operations research, design automation, control, etc. In this paper, a formal formulation of the problem of multicriteria equilibrium optimization is given, and an approach to solving this problem is examined.

Key words: multicriteria optimization, Pareto optimality, equilibrium solutions, sensitivity function, extraproximal method.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:12, 1912–1927

Bibliographic databases:

UDC: 519.626
Received: 10.05.2007

Citation: A. S. Antipin, “Multicriteria equilibrium programming: Extraproximal methods”, Zh. Vychisl. Mat. Mat. Fiz., 47:12 (2007), 1998–2013; Comput. Math. Math. Phys., 47:12 (2007), 1912–1927

Citation in format AMSBIB
\by A.~S.~Antipin
\paper Multicriteria equilibrium programming: Extraproximal methods
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 12
\pages 1998--2013
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 12
\pages 1912--1927

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    This publication is cited in the following articles:
    1. A. V. Zykina, “Inverse complementarity in a resource deficit model”, Comput. Math. Math. Phys., 48:11 (2008), 1971–1980  mathnet  crossref  mathscinet  isi
    2. Vasil'ev F.P., Antipin A.S., Artem'eva L.A., “Continuous extragradient method for a parametric multicriteria equilibrium programming problem”, Differ. Equ., 45:11 (2009), 1612–1620  crossref  mathscinet  zmath  isi  elib  scopus
    3. Vasilev F.P., Artemeva L.A., Antipin A.S., “Metod stabilizatsii dlya resheniya parametricheskoi mnogokriterialnoi zadachi ravnovesnogo programmirovaniya”, Vestn. Mosk. un-ta. Ser. 15: Vychislitelnaya matematika i kibernetika, 2009, no. 4, 15–21
    4. A. S. Antipin, L. A. Artem'eva, F. P. Vasil'ev, “Multicriteria equilibrium programming: the extragradient method”, Comput. Math. Math. Phys., 50:2 (2010), 224–230  mathnet  crossref  mathscinet  adsnasa  isi
    5. A. S. Antipin, L. A. Artem'eva, F. P. Vasil'ev, “Regularized extragradient method for solving parametric multicriteria equilibrium programming problem”, Comput. Math. Math. Phys., 50:12 (2010), 1975–1989  mathnet  crossref  adsnasa
    6. Vasilyev F.P., Antipin A.S., Artemieva L.A., “Regularized Continuous Extragradient Method for Solving a Parametric Multicriteria Equilibrium Programming Problem”, Doklady Mathematics, 82:2 (2010), 755–758  crossref  mathscinet  zmath  isi  elib  scopus
    7. Vasil'ev F.P., Antipin A.S., Artem'eva L.A., “Regularized continuous extragradient method for a multicriterial equilibrium programming problem”, Differ Equ, 46:11 (2010), 1584–1600  crossref  mathscinet  zmath  isi  scopus
    8. S. R. Aleeva, E. O. Yakubovich, “Ravnovesnoe programmirovanie i ego primenenie dlya nakhozhdeniya ravnovesiya po Neshu”, Vestnik ChelGU, 2013, no. 16, 6–20  mathnet
    9. L. A. Artem'eva, “Extragradient methods for searching for equilibrium points in the parametric problem of equilibrium programming”, Comput. Math. Math. Phys., 54:12 (2014), 1776–1787  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    10. 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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