Geodesic
Method of orthogonal simplexes and its applications to convex programming
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 610-622 
V. P. Bulatov. Method of orthogonal simplexes and its applications to convex programming. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 610-622. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a5/
@article{ZVMMF_2008_48_4_a5,
     author = {V. P. Bulatov},
     title = {Method of orthogonal simplexes and its applications to convex programming},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {610--622},
     year = {2008},
     volume = {48},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a5/}
}
TY  - JOUR
AU  - V. P. Bulatov
TI  - Method of orthogonal simplexes and its applications to convex programming
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 610
EP  - 622
VL  - 48
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a5/
LA  - ru
ID  - ZVMMF_2008_48_4_a5
ER  - 
%0 Journal Article
%A V. P. Bulatov
%T Method of orthogonal simplexes and its applications to convex programming
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 610-622
%V 48
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a5/
%G ru
%F ZVMMF_2008_48_4_a5

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

Numerical methods for solving a convex programming problem are considered whose guaranteed convergence rate depends only on the space dimension. On average, the ratio of the corresponding geometric progression is better than that in the basis model of ellipsoids or simplexes. Results of numerical experiments are presented.

[1] Bulatov V. P., Shepotko I. O., “Metod ortogonalnykh simpleksov v vypuklom programmirovanii”, Prikl. matem., SEI SO AN SSSR, Irkutsk, 1982

[2] Antsiferov E. G., Bulatov V. P., “Algoritm simpleksnykh pogruzhenii v vypuklom programmirovanii”, Zh. vychisl. matem. i matem. fiz., 27:3 (1987), 377–384 | MR

[3] Aschepkov L. T., Belov B. I., Bulatov V. P., Metody resheniya zadach matematicheskogo programmirovaniya i optimalnogo upravleniya, Nauka, Novosibirsk, 1984

[4] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983 | MR

[5] Yudin D. B., Nemirovskii A. C., “Informatsionnaya slozhnost i effektivnye metody resheniya vypuklykh ekstremalnykh zadach”, Ekonomika i matem. metody, 12:2 (1976), 357–369 | MR | Zbl

[6] Levin Yu. Ya., “Ob odnom algoritme minimizatsii vypuklykh funktsii”, Dokl. AN SSSR, 160:6 (1965), 1244–1247 | MR | Zbl

[7] Mityagin B. C., “Dva neravenstva dlya ob'emov vypuklykh tel”, Matem. zametki, 5:5 (1965), 20–25

[8] Khachiyan L. G., “Problemy optimalnykh algoritmov v vypuklom programmirovanii dekompozitsii i svertki”, Kompyuter i zadachi vybora, Nauka, M., 1989, 161–204 | MR

[9] Khachiyan L. G., “Polinomialnye algoritmy v lineinom programmirovanii”, Zh. vychisl. matem. i matem. fiz., 20:1 (1980), 51–69 | MR

[10] Shor N. Z., “Metody otsecheniya s rastyazheniem prostranstva dlya resheniya zadach vypuklogo programmirovaniya”, Kibernetika, 1977, no. 1, 94–95 | Zbl

[11] Bulatov V. P., Metody pogruzheniya v zadachakh optimizatsii, Nauka SO, Novosibirsk, 1977 | MR | Zbl

[12] Antsiferov E. G., Danilenko Yu. N., “Reshenie zadachi vypuklogo programmirovaniya modifitsirovannym metodom opornogo konusa”, Metody optimizatsii i ikh prilozh., Nauka SO, Novosibirsk, 1982, 32–35 | MR