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

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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. 
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     title = {On families of hyperplanes that separate polyhedra},
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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