Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {New variants of the generalized level method for minimization of convex nondifferentiable functions taking infinite values},
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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/

[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