@article{ZVMMF_1998_38_7_a7,
author = {A. S. Antipin},
title = {Splitting of the gradient approach for solving extreme inclusions},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1118--1132},
year = {1998},
volume = {38},
number = {7},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_7_a7/}
}
TY - JOUR AU - A. S. Antipin TI - Splitting of the gradient approach for solving extreme inclusions JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1998 SP - 1118 EP - 1132 VL - 38 IS - 7 UR - http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_7_a7/ LA - ru ID - ZVMMF_1998_38_7_a7 ER -
A. S. Antipin. Splitting of the gradient approach for solving extreme inclusions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 38 (1998) no. 7, pp. 1118-1132. http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_7_a7/
[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] 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
[3] Aubin J.-P., Frankowska H., Set valued analysis, Birkhäuser, Basel etc., 1990 | Zbl
[4] Golshtein E. G., Tretyakov N. V., Modifitsirovannye funktsii Lagranzha, Nauka, M., 1989
[5] Antipin A. S., “Sedlovye gradientnye protsessy, upravlyaemye s pomoschyu obratnykh svyazei”, Avtomatika i telemekhan., 1994, no. 3, 12–23 | MR | Zbl
[6] Antipin A. S., “Obratnaya zadacha optimizatsii: postanovka zadachi i podkhody k ee resheniyu”, Obratnye zadachi matem. programmirovaniya, VTs RAN, M., 1992, 4–58
[7] Migdalas A., Pardalos P. M., “Editorial: hierarchical and bilevel programming”, J. Global Optimizat., 8 (1996), 209–215 | DOI | MR
[8] Outrata J. V., “On optimization problems with variational inequality constraints”, SIAM J. Optimizat., 4:2 (1994), 340–357 | DOI | MR | Zbl
[9] Harker P. T., Pang J. S., “Finite dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications”, Math. Program., 48 (1990), 161–220 | DOI | MR | Zbl
[10] Kaplan A., Tichatschke R., “Multi-step proximal method for variational inequalities with monotone operators”, Recent Advances in Optimizat., Lect. Notes in Econ. and Math. Systems, 452, Springer, Berlin, 1997, 138–153 | Zbl
[11] Blum E., Oettli W., “From optimization and variational inequalities to equilibrium problems”, Math. Student., 63:1–4 (1993), 1–23
[12] Antipin A. S., “O differentsialnykh gradientnykh metodakh prognoznogo tipa dlya vychisleniya nepodvizhnykh tochek ekstremalnykh otobrazhenii”, Differents. ur-niya, 31:11 (1995), 1786–1795 | MR | Zbl
[13] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1988
[14] Rosen J. B., “Existence and uniqueness of equilibrium points for concave $n$-person games”, Econometrica, 33:3 (1965), 520–534 | DOI | MR | Zbl
[15] Monderer D., Shapley L. S., “Potential games”, Games and Economic Behavior, 14 (1996), 124–143 | DOI | MR | Zbl
[16] Polyak B. T., Vvedenie v optimizatsiyu, Fizmatgiz, M., 1973
[17] Antipin A. S., “Ob otsenkakh skorosti skhodimosti metoda proektsii gradienta”, Izv. vuzov. Matematika, 1995, no. 6, 16–24 | MR | Zbl
[18] Antipin A. S., “Upravlyaemye proksimalnye differentsialnye sistemy dlya resheniya sedlovykh zadach”, Differents. ur-niya, 28:11 (1992), 1846–1861 | MR | Zbl
[19] Belenkii V. Z., Volkonskii V. A., Iterativnye metody v teorii igr i programmirovanii, Nauka, M., 1974
[20] Rokafellar R., Vypuklyi analiz, Mir, M., 1973
[21] Fan Ky, “A minimax inequality and applications”, Inequalities III, Acad. Press, New York, 1972, 103–113
[22] Korpelevich G. M., “Ekstragradientnyi metod dlya otyskaniya sedlovykh tochek i drugikh zadach”, Ekonomika i matem. metody, 12:4 (1976), 747–756 | MR | Zbl
[23] Antipin A. S., “Ob odnom metode poiska sedlovykh tochek modifitsirovannoi funktsii Lagranzha”, Ekonomika i matem. metody, 13:3 (1977), 560–565 | MR | Zbl
[24] Antipin A. S., “Ravnovesnoe programmirovanie: metody gradientnogo tipa”, Avtomatika i telemekhan., 1997, no. 8, 166–178 | MR