Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 2037-2054
Citer cet article
N. A. Sokolov. New variants of the generalized level method for minimization of convex nondifferentiable functions taking infinite values. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 2037-2054. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a6/
@article{ZVMMF_2007_47_12_a6,
author = {N. A. Sokolov},
title = {New variants of the generalized level method for minimization of convex nondifferentiable functions taking infinite values},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {2037--2054},
year = {2007},
volume = {47},
number = {12},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a6/}
}
TY - JOUR
AU - N. A. Sokolov
TI - New variants of the generalized level method for minimization of convex nondifferentiable functions taking infinite values
JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY - 2007
SP - 2037
EP - 2054
VL - 47
IS - 12
UR - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a6/
LA - ru
ID - ZVMMF_2007_47_12_a6
ER -
%0 Journal Article
%A N. A. Sokolov
%T New variants of the generalized level method for minimization of convex nondifferentiable functions taking infinite values
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 2037-2054
%V 47
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a6/
%G ru
%F ZVMMF_2007_47_12_a6
New variants of the generalized level method for minimization of convex Lipschitz functions on a compact set with a nonempty interior are proposed. These variants include the well-known generalized and classical level methods. For the new variants, an estimate of the convergence rate is found, including the variants in which the auxiliary problems are solved approximately.
[1] Ber K., Golshtein E. G., Sokolov H. A., “Ob ispolzovanii metoda urovnei dlya minimizatsii vypuklykh funktsii, ne vse znacheniya kotorykh konechny”, Ekonomika i matem. metody, 36:4 (2000), 95–107
[2] Beer K., Gol'shtein E. G., Sokolov N. A., “Minimization of a nondifferentiable convex function defined not everywhere”, Optimization, 51:6 (2002), 819–840 | DOI | MR | Zbl
[3] Lemaréchal C., Nemirovskii A., Nesterov Yu., “New Variants of Bundle Methods”, Math. Program., 69 (1995), 111–147 | DOI | MR | Zbl
[4] Golshtein E. G., Nemirovskii A. C., Nesterov Yu. E., “Metod urovnei, ego obobscheniya i prilozheniya”, Ekonomika i matem. metody, 31:3 (1995), 164–180
[5] Sokolov H. A., Programma pryamoi dekompozitsii (PDLEV) zadach lineinogo programmirovaniya, osnovannoi na metode urovnei, Preprint # WP/2001/114, TsEMI RAN, M., 2001