The Lagrange multiplier technique for variational inequalities
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 41 (2001) no. 9, pp. 1344-1357 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_2001_41_9_a7,
     author = {I. V. Konnov},
     title = {The {Lagrange} multiplier technique for variational inequalities},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1344--1357},
     year = {2001},
     volume = {41},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2001_41_9_a7/}
}
TY  - JOUR
AU  - I. V. Konnov
TI  - The Lagrange multiplier technique for variational inequalities
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2001
SP  - 1344
EP  - 1357
VL  - 41
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2001_41_9_a7/
LA  - ru
ID  - ZVMMF_2001_41_9_a7
ER  - 
%0 Journal Article
%A I. V. Konnov
%T The Lagrange multiplier technique for variational inequalities
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2001
%P 1344-1357
%V 41
%N 9
%U http://geodesic.mathdoc.fr/item/ZVMMF_2001_41_9_a7/
%G ru
%F ZVMMF_2001_41_9_a7
I. V. Konnov. The Lagrange multiplier technique for variational inequalities. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 41 (2001) no. 9, pp. 1344-1357. http://geodesic.mathdoc.fr/item/ZVMMF_2001_41_9_a7/

[1] Hestenes M. R., “An indirect sufficiency proof for the problem of Bolza in nonparametric form”, Trans. Amer. Math. Soc., 62:3 (1947), 509–535 | DOI | MR | Zbl

[2] Errou K. Dzh., Solou P. M., “Gradientnye metody otyskaniya uslovnogo maksimuma pri oslablennykh predpolozheniyakh”, V kn.: Errou K. Dzh., Gurvits L., Udzava X., Issledovaniya po lineinomu i nelineinomu programmirovaniyu, Izd-vo inostr. lit., M., 1962, 246–262

[3] Powell M. J. D., “A method for nonlinear constraints in minimization problems”, Optimization, Acad. Press, London–New York, 1969, 283–298 | MR

[4] Hestenes M. R., “Multiplier and gradient methods”, J. Optimizat. Theory and Appl., 4:5 (1969), 303–320 | DOI | MR | Zbl

[5] Rockafellar R. T., “The multiplier method of Hestenes and Powell applied to convex programming”, J. Optimizat. Theory and Appl., 12:6 (1973), 555–562 | DOI | MR | Zbl

[6] Antipin A. S., Metody nelineinogo programmirovaniya, osnovannye na pryamoi i dvoistvennoi modifikatsii funktsii Lagranzha, Preprint, VNIISI, M., 1979

[7] Evtushenko Yu. G., Metody resheniya ekstremalnykh zadach i ikh primenenie v sistemakh optimizatsii, Nauka, M., 1982 | MR | Zbl

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

[9] Bertsekas D., Uslovnaya optimizatsiya i metody mnozhitelei Lagranzha, Nauka, M., 1989

[10] Golshtein E. G., Tretyakov N. V., Modifitsirovannye funktsii Lagranzha, Nauka, M., 1989 | MR

[11] Baiokki K., Kapelo A., Variatsionnye i kvazivariatsionnye neravenstva. Prilozhenie k zadacham so svobodnoi granitsei, Nauka, M., 1988 | MR

[12] Harker P. T., Pang J.-S., “Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications”, Math. Program., 48:2 (1990), 161–220 | DOI | MR | Zbl

[13] Uryasev S. P., Adaptivnye algoritmy stokhasticheskoi optimizatsii i teorii igr, Nauka, M., 1990 | MR

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

[15] Antipin A. S., “Ravnovesnoe programmirovanie: proksimalnye metody”, Zh. vychisl. matem. i matem. fiz., 37:11 (1997), 1327–1339 | MR | Zbl

[16] Antipin A. S., “Ravnovesnoe programmirovanie: metody gradientnogo tipa”, Avtomatika i telemekhan., 1997, no. 8, 125–137 | MR | Zbl

[17] Gabay D., “Application of the method of multipliers to variational inequalities”, Augmented Lagrangian Methods: Applic. Numer. Solution of Boundary-Value Problems, North-Holland, Amsterdam, 1983, 299–331

[18] Crouzeix J.-P., “Pseudomonotone variational inequality problems: existence of solutions”, Math. Program., 78:3 (1997), 305–314 | DOI | MR | Zbl

[19] Sukharev A. G., Timokhov A. V., Fedorov V. V., Kurs metodov optimizatsii, Nauka, M., 1986 | MR | Zbl

[20] Bakushinskii A. B., Goncharskii A. V., Iterativnye metody resheniya nekorrektnykh zadach, Nauka, M., 1989 | MR