An extraproximal method for solving equilibrium programming problems and games
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 1969-1990 Cet article a éte moissonné depuis la source Math-Net.Ru

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For equilibrium programming problems and two-person games defined on simple sets or sets given by functional inequality constraints, an extraproximal method is proposed and examined. The convergence of this method is proved.
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A. S. Antipin. An extraproximal method for solving equilibrium programming problems and games. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 1969-1990. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a6/

[1] Antipin A. S., “O skhodimosti i otsenkakh skorosti skhodimosti proksimalnykh metodov k nepodvizhnym tochkam ekstremalnykh otobrazhenii”, Zh. vychisl. matem. i matem. fiz., 35:5 (1995), 688–704 | MR | Zbl

[2] Aubin J.-P., Frankowska H., Set valued analysis, Birkhauser, Boston etc., 1990 | MR | Zbl

[3] Antipin A., “Differential equations for equilibrium problems with coupled constraints”, Nonlinear Analys., 47 (2001), 1833–1844 | DOI | MR | Zbl

[4] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002

[5] Antipin A. S., “Ekstrapolyatsionnye metody vychisleniya sedlovoi tochki funktsii Lagranzha i ikh primenenie k zadacham s blochno-separabelnoi strukturoi”, Zh. vychisl. matem. i matem. fiz., 1:1 (1986), 150–151

[6] Facchinei F., Pang J.-Sh., Finite-dimensional variational inequalities and complementarity problems, v. I; II, Springer, New York, 2003

[7] Antipin A. S., “Vychislenie nepodvizhnykh tochek ekstremalnykh otobrazhenii pri pomoschi metodov gradientnogo tipa”, Zh. vychisl. matem. i matem. fiz., 37:1 (1997), 42–53 | MR | Zbl

[8] Konnov I., Combined relaxation methods for variational inequalities, Springer, Berlin etc., 2001 | MR

[9] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983 | MR

[10] Antipin A. S., Gradientnyi i ekstragradientnyi podkhody v bilineinom ravnovesnom programmirovanii, VTs RAN, M., 2002, 132 pp. www.ccas.ru/antipin

[11] Rosen J. B., “Existance and uniqueness of equilibrium points for concave N-person games”, Econometrica, 33:3 (1965), 520–534 | DOI | MR | Zbl

[12] Zukhovitsky S. I., Polyak R. A., Primak M. E., “Concave N-person games (numerical methods)”, Economica i Matem. Metody, 7:6 (1971), 888–900 | MR

[13] Flam S. D., “Equilibrium, evolutionary stability and gradient dynamics”, Internat. Game Theory Rev., 4:4 (2002), 1–14 | MR

[14] Bakushinsky A., Goncharsky A., Ill-posed problems: Theory and applications, Kluwer, Dordrecht, 1994

[15] Mangasarian O. L., Stone H., “Two-person nonzero-sum games and quadratic programming”, J. Math. Analys. and Appl., 9 (1964), 348–355 | DOI | MR | Zbl

[16] Mills H., “Equilibrium points in finite games”, J. Soc. Indust. Appl. Math., 8:2 (1960), 397–402 | DOI | MR | Zbl

[17] Garcia C. B., Zangwill W. I., Pathways to solutions, fixed points, and equilibria, Prentice-Hall, Englewood Cliffs, N.J., 1981

[18] Hansen T., “On the approximation of Nash equilibrium points in an N-person noncooperative game”, SIAM J. Appl. Math., 26:3 (1974), 622–637 | DOI | MR | Zbl

[19] Stengel B., “Computing equilibria for two-person games”, Handbook of Game Theory, v. 3, North-Holland, Amsterdam, 2002, 1–39

[20] Nash J. F. Jr., “Equilibrium points in N-person game”, Proc. Nat. Acad. Sci., USA, 36 (1950), 48–49 | DOI | MR | Zbl

[21] Antipin A. S., “Equilibrium programming problem: prox-regularization and prox-methods”, Recent Advances in Optimizat., Lect. Notes in Economics and Math. Systems, Springer, 1997 | MR