Geodesic
Iterative solution of matrix games by the methods of grid variational inequalities
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1367-1380
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A new approach to the approximate solution of matrix games is proposed. It is based on the reduction of the original problem to a variational inequality of a special form. In particular, this makes it possible to design preconditioned iterative methods, which proved to be effective as a tool for the numerical solution of large and ill-conditioned systems of linear algebraic equations. 
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E. V. Chizhonkov. Iterative solution of matrix games by the methods of grid variational inequalities. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1367-1380. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a2/

[1] Karmarkar N., “A new polinomial-time algorithm for linear programming”, Combinatorica, 4:4 (1984), 373–395 | DOI | MR | Zbl

[2] Wright M. H., “The interior-point revolution in optimization: history, recent developments, and lasting consequences”, Bull. Amer. Math. Soc., 42:1 (2004), 39–56 | DOI | MR

[3] Nemirovski A. S., Todd M. J., “Interior-point methods for optimization”, Acta Numerica, 17 (2008), 191–234 | DOI | MR | Zbl

[4] Vasilev F. P., Ivanitskii A. Yu., Lineinoe programmirovanie, Faktorial, M., 1998 | MR

[5] Khachiyan L. G., Slozhnost zadach lineinogo programmirovaniya, Znanie, M., 1987 | MR

[6] Belenkii V. Z., Volkonskii V. A., Ivanov S. A. i dr., Iterativnye metody v teorii igr i programmirovaniya, Nauka, M., 1974 | MR

[7] Dyakonov E. G., “O primenenii ekvivalentnykh po spektru operatorov dlya resheniya raznostnykh analogov silno ellipticheskikh sistem”, Dokl. AN SSSR, 163:6 (1965), 1314–1317

[8] Dyakonov E. G., “O postroenii iteratsionnykh metodov na osnove ispolzovaniya operatorov, ekvivalentnykh po spektru”, Zh. vychisl. matem. i matem. fiz., 6:1 (1966), 12–34

[9] Chizhonkov E. V., Relaksatsionnye metody resheniya sedlovykh zadach, IVM RAN, M., 2002

[10] Konnov I. V., Metody resheniya konechnomernykh variatsionnykh neravenstv. Kurs lektsii, DAS, Kazan, 1998 | MR

[11] Lapin A. V., Iteratsionnye metody resheniya setochnykh variatsionnykh neravenstv, Izd-vo Kazansk. gos. un-ta, Kazan, 2008

[12] Neiman Dzh., Morgenshtern O., Teoriya igr i ekonomicheskoe povedenie, Nauka, M., 1970 | MR

[13] Vorobev N. N., Teoriya igr dlya ekonomistov-kibernetikov, Nauka, M., 1985 | MR

[14] N. N. Vorobev (red.), Matrichnye igry, Gosfizmatlit, M., 1961 | MR

[15] Gale D., Kuhn H. W., Tucker A. W., “On symmetric games”, Contributions to the Theory of Games, v. 1, Ann. Math. Study, 24, Princeton Univ. Press, Princeton, New York, 1950, 81–87 | MR

[16] Gaas S. I., Zafra P. M., Qui Z., “Modified fictitious play”, Naval Res. Logistics, 43 (1996), 955–977 | 3.0.CO;2-C class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR

[17] Washburn A., “A new kind of fictitious play”, Naval Res. Logistics, 48 (2001), 269–280 | DOI | MR

[18] Voevodin V. V., Kuznetsov Yu. A., Matritsy i vychisleniya, Nauka, M., 1984 | MR

[19] Lebedev V. I., Funktsionalnyi analiz i vychislitelnaya matematika, Fizmatlit, M., 2005

[20] Dyakonov E. G., “O nekotorykh klassakh sedlovykh gradientnykh metodov”, Vychisl. protsessy i sistemy, 5, Nauka, M., 1987, 101–115 | MR

[21] Glovinski R., Lions Zh.-L., Tremoler R., Chislennoe issledovanie variatsionnykh neravenstv, Mir, M., 1979 | MR

[22] Parlett B., Simmetrichnaya problema sobstvennykh znachenii. Chislennye metody, Mir, M., 1983 | MR | Zbl

[23] Vaserstein L. N., Matrix games, linear programming, and linear approximation, 27 Jan 2006, arXiv: math.cs/0609056v1 | Zbl