Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2021 | OriginalPaper | Chapter

10. Finding Nonlinear Equilibrium

Author : Roman A. Polyak

Published in: Introduction to Continuous Optimization

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Optimization problems, finding a saddle point of a convex–concave function, matrix games, J. Nash equilibrium of n-person concave game, Walras–Wald equilibrium, finding nonlinear equilibrium (NE) for optimal resource allocation (ORA), and nonlinear input–output equilibrium (NIOE) are all particular cases of general nonlinear equilibrium (NE) problem.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Lagrangian Transformation and Interior Ellipsoid Methods
next chapter Applications and Numerical Results
Literature
Antipin, A.: The Gradient and Exstragradient Approaches in Bilinear Equilibrium Programming A. In: Dorodnizin Computing Center RAS (in Russian) (2002)
Ashmanov, S.: Introduction into Mathematical Economics. Moscow, Nauka (1984)MATH
Bakushinskij, A., Polyak, B.: On the solution of variational inequalities. Sov. Math. Doklady 14, 1705–1710 (1974)
Censor, Y., Gibali, A., Reich, S.: The subgradient extragradient method for solving variational inequalities in hilbert space. J. Optim. Theory Appl. 148, 318–335 (2011)MathSciNetCrossRef
Dantzig, G.: Linear Programming and Extensions. Princeton University, Princeton (1963)MATH
Dorfman, R., Samuelson, R.: Solow Linear Programming and Economic Analysis. Mc Graw-Hill, New York (1958)MATH
Farcchinei, F., Pang, J.: Finite—Dimentional Variational Inequalities and Complementarity Problems, vol 1 and 2. Springer, Berlin (2003)
Gale, D.: The Theory of Linear Economic Models, NY (1960)
Gantmacher, D.: The Theory of Matrices, ANS (1959)
Goldstein, A.: Convex programming in gilbert space. Bull. Am. Math Soc. 70, 709–710 (1964)MATH
Gusev, M., Evans, D.: The fastest matrix vector multiplication. Parallel Algorithms Appl. 1(1), 57–67 (1993)CrossRef
Iusem, A., Svaiter, B.A.: Variant of Korpelevich’s method for the variational inequalities with a new search strategy. Optimization 42(4), 309–321 (1997)MathSciNetCrossRef
Kantorovich, L.: Mathematical methods of organizing and planning production. Manage. Sci. 6(4), 366–422 (1939). JSTOR 2627082
Kantorovich, L.:The Best Use of Economic Resources. Pergamon Press, New York (1959)
Khobotov, E.: A modification of the extragradient method for solving variational inequalities and some optimization problems (Russian). Zh. Vychisl. Mat. i Mat Fiz. 27(10), 1462–1473, 1957 (1987)
Konnov, I.: Equilibrium Models and Variational Inequalities, vol 210. Elsevier, Amsterdam (2007)MATH
Korpelevich, G.: Extragradient method for finding saddle points and other problems. Matecon 12(4), 747–756 (1976)MathSciNetMATH
Kuhn, H.: On a theorem of wald, linear inequalities and related systems. In: Annals of Mathematics Studies, vol. 38. Princeton University, Princeton, pp. 265–273 (1956)
Lancaster, K.: Mathematical Economics. The Macmillan Company, New York (1968)MATH
Leontief, W.: Input-Output Economics. Oxford University Press, Oxford (1966)
Levitin, E., Polyak, B.: Minimization methods in the presence of constraints. Z. Vycisl. Mat. i Mat Fizz 6, 787–823 (1966)MathSciNetMATH
Nash, J.: Non-cooperative games. Ann. of Math. 54(2), MR0043432(13, 261g) (1951)
Neumann, J.: Zur Theorie der Gesellschaftsspiele. Math. Ann. 100, 295–320 (1928)
Polyak, R.: On finding a fixed point of a class of set-valued mappings. Dokl. Akad. Nauk SSSR 242(6), 1284–1288 (1978)
Polyak, R.: Finding generalized Warlas-Wald equilibrium. Methods Funct. Anal. Topology 14(3), 242–254 (2008)MathSciNetMATH
Polyak, R.: Nonlinear equilibrium for optimal resources allocation. In: Contemporary Mathematics, vol. 636. AMS, New York, pp. 1–17 (2015)
Polyak, R.: Nonlinear input-output equilibrium. In: Contemporary Mathematics, vol. 659. AMS, New York (2016)
Polyak, R., Primak, M.: Methods of controlling sequences for solving equilibrium problems, Part 1. Cibernetics 13(2), 92–101 (1977a). (English translation available)
Polyak, R., Primak, M.: Methods of controlling sequences for solving equilibrium problems, Part 2. Cibernetics 13(4), 56–62 (1977b). (English translation available)
Rosen, J.: Existence and uniqueness of equilibrium points for concave n-persone games. Econometrica 33, 520–534 (1965)MathSciNetCrossRef
Wang, W., Carreira–Perpinan, M.: Projection onto the Probability Simplex: An Efficient Algorithm with a Simple Proof and an Application (2013). arXiv:1309.1541 [cs LG]
Zukhovitsky, S., Polyak, R., Primak, M.: Two methods for finding equilibrium of N-person concave games. Soviet Math. Dokl. 10(2) (1969)
Zukhovitsky, S., Polyak, R., Primak, M.: N-person concave games and one production model. Soviet Math. Dokl. 11(2), (1970)
Zukhovitsky, S., Polyak, R., Primak, M.: Concave N-Person Games: Numerical Methods, MAKETON (1973). (English translation available)
Metadata
Title
Finding Nonlinear Equilibrium
Author
Roman A. Polyak
Copyright Year
2021
Book
Introduction to Continuous Optimization

Print ISBN: 978-3-030-68711-3

Electronic ISBN: 978-3-030-68713-7

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-68713-7_10

Premium Partner

    Image Credits