Geodesic
A proximal method for solving quasi-variational inequalities
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2022-2026 
N. Mijailović; M. Jaćimović. A proximal method for solving quasi-variational inequalities. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2022-2026. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a4/
@article{ZVMMF_2015_55_12_a4,
     author = {N. Mijailovi\'c and M. Ja\'cimovi\'c},
     title = {A proximal method for solving quasi-variational inequalities},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2022--2026},
     year = {2015},
     volume = {55},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a4/}
}
TY  - JOUR
AU  - N. Mijailović
AU  - M. Jaćimović
TI  - A proximal method for solving quasi-variational inequalities
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 2022
EP  - 2026
VL  - 55
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a4/
LA  - ru
ID  - ZVMMF_2015_55_12_a4
ER  - 
%0 Journal Article
%A N. Mijailović
%A M. Jaćimović
%T A proximal method for solving quasi-variational inequalities
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 2022-2026
%V 55
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a4/
%G ru
%F ZVMMF_2015_55_12_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

Proximal methods for solving quasi-variational inequalities (an iterative and a continuous one) are examined, and conditions for these methods to converge are found.

[1] Antipin A. S., “Upravlyaemye proksimalnye differentsialnye sistemy dlya resheniya sedlovykh zadach”, Differents. ur-niya, 28:11 (1992), 1846–1861 | MR | Zbl

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

[3] Rockafellar R. T., “Monotone operators and the proximal point algorthm”, SIAM J. Control and Optimization, 1976, 205–217 | MR

[4] Lemaire B., “The proximal algorithm”, Intern. Series of Numer. Mathem., 87, Birkhäuser Verlag, Basel, 1989, 1–68 | MR

[5] Nesterov Yu., Scrimali L., Solving strongly monotone variational and quasi-variational inequalities, Core discussion paper No 2006/17

[6] Noor M. A., Oettli W., “On general nonlinear complementarity problems and quasi equilibria”, Le Mathematiche, XLIX (1994), 313–331 | MR | Zbl

[7] Vasilev F. P., Metody optimizatsii, v. I, Izd-vo MTsMNO, M., 2011