Geodesic
On families of hyperplanes that separate polyhedra
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 238-253
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of constructing a family of hyperplanes that separate two disjoint nonempty polyhedra is examined. the polyhedra are given by systems of linear inequalities or by systems of linear equalities with nonnegative variables. constructive algorithms for solving this problem are presented. the construction of separating hyperplanes relies heavily on theorems of the alternative. 
@article{ZVMMF_2005_45_2_a6,
     author = {A. I. Golikov and Yu. G. Evtushenko and S. Ketabchi},
     title = {On families of hyperplanes that separate polyhedra},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {238--253},
     year = {2005},
     volume = {45},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a6/}
}
TY  - JOUR
AU  - A. I. Golikov
AU  - Yu. G. Evtushenko
AU  - S. Ketabchi
TI  - On families of hyperplanes that separate polyhedra
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2005
SP  - 238
EP  - 253
VL  - 45
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a6/
LA  - ru
ID  - ZVMMF_2005_45_2_a6
ER  - 
%0 Journal Article
%A A. I. Golikov
%A Yu. G. Evtushenko
%A S. Ketabchi
%T On families of hyperplanes that separate polyhedra
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 238-253
%V 45
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a6/
%G ru
%F ZVMMF_2005_45_2_a6
A. I. Golikov; Yu. G. Evtushenko; S. Ketabchi. On families of hyperplanes that separate polyhedra. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 238-253. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a6/

[1] Eremin I. I., Teoriya lineinoi optimizatsii, UrO RAN, Ekaterinburg, 1998

[2] Golikov A. I., Evtushenko Yu. G., “Teoremy ob alternativakh i ikh primenenie v chislennykh metodakh”, Zh. vychisl. matem. i matem. fiz., 43:3 (2003), 354–375 | MR | Zbl

[3] Vasilev F. P., Ivanitskii A. Yu., Lineinoe programmirovanie, Faktorial, M., 2003 | MR

[4] Mangasarian O. L., “A finite Newton method for classification”, Optimizat. Meth. and Software, 17 (2002), 913–930 | DOI | MR

[5] Mangasarian O. L., “A Newton method for linear programming”, J. Optimizat. Theory and Appl., 121 (2004), 1–18 | DOI | MR | Zbl

[6] Kanzow C., Qi H., Qi L., “On the minimum norm solution of linear programs”, J. Optimizat. Theory and Appl., 116 (2003), 333–345 | DOI | MR | Zbl