Geodesic
A cutting method and construction of mixed minimization algorithms on its basis
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 4, pp. 14-24 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We propose a cutting method for conditional minimization of convex functions. We show that it is possible to construct mixed minimization algorithms without losing their convergence on the basis of this method with the assistance of other convex programming methods. The qualitative evaluation of an approximation set, involved in this method, allows us to periodically update the approximation sets in the proposed method and mixed algorithms with the purpose of simplifying the problems of construction of iteration points.
Keywords: approximation set, cutting plane, sequence of approximation, conditional minimization, mixed algorithms.
Mots-clés : convergence 
@article{UZKU_2014_156_4_a1,
     author = {I. Ya. Zabotin and O. N. Shulgina and R. S. Yarullin},
     title = {A cutting method and construction of mixed minimization algorithms on its basis},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {14--24},
     year = {2014},
     volume = {156},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2014_156_4_a1/}
}
TY  - JOUR
AU  - I. Ya. Zabotin
AU  - O. N. Shulgina
AU  - R. S. Yarullin
TI  - A cutting method and construction of mixed minimization algorithms on its basis
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2014
SP  - 14
EP  - 24
VL  - 156
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/UZKU_2014_156_4_a1/
LA  - ru
ID  - UZKU_2014_156_4_a1
ER  - 
%0 Journal Article
%A I. Ya. Zabotin
%A O. N. Shulgina
%A R. S. Yarullin
%T A cutting method and construction of mixed minimization algorithms on its basis
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2014
%P 14-24
%V 156
%N 4
%U http://geodesic.mathdoc.fr/item/UZKU_2014_156_4_a1/
%G ru
%F UZKU_2014_156_4_a1
I. Ya. Zabotin; O. N. Shulgina; R. S. Yarullin. A cutting method and construction of mixed minimization algorithms on its basis. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 4, pp. 14-24. http://geodesic.mathdoc.fr/item/UZKU_2014_156_4_a1/

[1] Zangvill U. I., Nelineinoe programmirovanie, Sov. radio, M., 1973, 312 pp.

[2] Bulatov V. P., Metody pogruzheniya v zadachakh optimizatsii, Nauka, Novosibirsk, 1977, 161 pp. | MR

[3] Zabotin I. Ya., “O nekotorykh algoritmakh pogruzhenii-otsechenii dlya zadachi matematicheskogo programmirovaniya”, Izv. Irkutskogo gos. un-ta. Ser. Matem., 4:2 (2011), 91–101 | Zbl

[4] Nesterov Yu. E., Vvedenie v vypukluyu optimizatsiyu, MTsNMO, M., 2010, 274 pp.

[5] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983, 384 pp. | MR

[6] Zabotin I. Ya., Yarullin R. S., “Ob odnom podkhode k postroeniyu algoritmov otsechenii s otbrasyvaniem otsekayuschikh ploskostei”, Izv. vuzov. Matem., 2013, no. 3, 74–79 | Zbl

[7] Zabotin I. Ya., Yarullin R. S., “Metod otsechenii c obnovleniem pogruzhayuschikh mnozhestv i otsenki tochnosti resheniya”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 2, 2013, 54–64

[8] Zabotin I. Ya., Yarullin R. S., “Algoritm otsechenii s approksimatsiei nadgrafika”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 4, 2013, 48–54

[9] Vasilev F. P., Metody optimizatsii, v 2 kn., Kn. 1, MTsNMO, M., 2011, 620 pp.

[10] Konnov I. V., Nelineinaya optimizatsiya i variatsionnye neravenstva, Kazan. un-t, Kazan, 2013, 508 pp.