Geodesic
Universal extremum of hyperplanes in some optimization problems
Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 3, pp. 91-106.

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

This paper is concerned with the minimum distance between a point and a polyhedrons of some class in the $R^n$ vector space supplied with different symmetrical norms. We find all hyperplanes where for all polyhedrons the point of Euclidean norm minimum is also one of the nearest points in any symmetrical norm. It simplifies the choice of criterion in some optimization problems.
Mots-clés : Norm, Euclidean norm, distance
Keywords: symmetrical norm, hyperplane, class of hyperplanes, class of polyhedrons, $R^n$ space, optimization functions, optimization problems. 
@article{MAIS_2010_17_3_a6,
     author = {N. P. Fedotova},
     title = {Universal extremum of hyperplanes in some optimization problems},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {91--106},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2010_17_3_a6/}
}
TY  - JOUR
AU  - N. P. Fedotova
TI  - Universal extremum of hyperplanes in some optimization problems
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2010
SP  - 91
EP  - 106
VL  - 17
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2010_17_3_a6/
LA  - ru
ID  - MAIS_2010_17_3_a6
ER  - 
%0 Journal Article
%A N. P. Fedotova
%T Universal extremum of hyperplanes in some optimization problems
%J Modelirovanie i analiz informacionnyh sistem
%D 2010
%P 91-106
%V 17
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2010_17_3_a6/
%G ru
%F MAIS_2010_17_3_a6
N. P. Fedotova. Universal extremum of hyperplanes in some optimization problems. Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 3, pp. 91-106. http://geodesic.mathdoc.fr/item/MAIS_2010_17_3_a6/

[1] V. I. Berdyshev, L. V. Petrak, Approksimatsiya funktsii, szhatie chislennoi informatsii, prilozheniya, UrO RAN, Ekaterinburg, 1999 | MR

[2] I. Ts. Gokhberg, M. G. Krein, Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostrnstve, Nauka, M., 1965 | MR

[3] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972

[4] N. M. Korshunova, V. S. Rublev, “Zadacha tselochislennogo sbalansirovaniya matritsy”, Sovremennye problemy matematiki i informatiki, 3 (2000), 145–150, Yaroslavl

[5] P. Rokafellar, Vypuklyi analiz, Mir, M., 1973

[6] V. S. Rublev, N. B. Chaplygina, “Vybor kriteriya optimizatsii v zadache o ravnomernom naznachenii”, Diskretnaya matematika, 17:4 (2005), 150–157 | MR | Zbl

[7] V. S. Rublev, N. B. Chaplygina, “O nekotoroi kharakternoi tochke odnogo klassa mnogogrannikov v simmetricheskikh prostranstvakh”, DAN, 407:2 (2006), 176–178 | MR