Coordinate relaxation methods for multivalued complementarity problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 1021-1036 Cet article a éte moissonné depuis la source Math-Net.Ru

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Methods of the Jacobi and Gauss–Seidel type with underrelaxation and a combined method of the splitting type are proposed for complementarity problems with multivalued mappings. The convergence of these methods to the solution is proved under the conditions that the basic mapping is upper off-diagonal antitone and the feasible set is nonempty. The numerical results obtained for test examples are presented.
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I. V. Konnov. Coordinate relaxation methods for multivalued complementarity problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 1021-1036. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a6/

[1] Berschanskii Ya. M., Meerov M. V., “Teoriya i metody resheniya zadach dopolnitelnosti”, Avtomatika i telemekhan., 1983, no. 6, 5–31

[2] Cottle R. W., Pang J. S., Stone R. E., The linear complementarity problem, Acad. Press, Boston, 1992 | MR | Zbl

[3] Isac G., Complementarity problems, Springer, Berlin, 1992 | MR | Zbl

[4] Facchinei F., Pang J.-S., Finite-dimensional variational inequalities and complementarity problems, two volumes, Springer, Berlin, 2003

[5] Konnov I. V., Equilibrium models and variational inequalities, Elsevier, Amsterdam, 2007 | MR

[6] Nikaido X., Vypuklye struktury i matematicheskaya ekonomika, Mir, M., 1972

[7] Polterovich V. M., Spivak V. A., “Otobrazheniya s valovoi zamenimostyu v teorii ekonomicheskogo ravnovesiya”, Itogi nauki i tekhn. Sovremennye probl. matem., 19, VINITI, M., 1982, 111–154 | MR

[8] Lapin A. V., “Domain decomposition and parallel solution of free boundary problems”, Tr. matem. tsentra im. N. I. Lobachevskogo, 13, Izd-vo “DAS”, Kazan, 2001, 90–126

[9] Konnov I. V., “An extension of the Jacobi algorithm for multi-valued mixed complementarity problems”, Optimization, 56:3 (2007), 399–416 | DOI | MR | Zbl

[10] Konnov I. V., Kostenko T. A., “Mnogoznachnaya smeshannaya zadacha dopolnitelnosti”, Izv. vuzov. Matematika, 2004, no. 12, 28–36 | MR

[11] Konnov I. V., “Obobschenie algoritma Yakobi dlya zadachi dopolnitelnosti v usloviyakh mnogoznachnosti”, Zh. vychisl. matem. i matem. fiz., 45:7 (2005), 1167–1173 | MR | Zbl

[12] Konnov I. V., “Iterative algorithms for mulit-valued inclusions with $Z$ mappings”, J. Comput. and Appl. Math., 206:1 (2007), 358–365 | DOI | MR | Zbl

[13] Ortega Dzh., Reinboldt V., Iteratsionnye metody resheniya nelineinykh sistem uravnenii so mnogimi neizvestnymi, Mir, M., 1975 | MR

[14] Pang J.-S., Chan D., “Iterative methods for variational and complementarity problems”, Math. Program., 24:3 (1982), 284–313 | DOI | MR | Zbl

[15] More J. J., “Classes of functions and feasibility conditions in nonlinear complementarity problems”, Math. Program., 6:3 (1974), 327–338 | DOI | MR | Zbl

[16] Tamir A., “Minimality and complementarity problems associated with $Z$-functions and $M$-functions”, Math. Program., 7:1 (1974), 17–31 | DOI | MR | Zbl