Geodesic
Carathéodory’s Theorem with Linear Constraints
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 189-191

Voir la notice de l'article provenant de la source Cambridge University Press

Carathéodory has shown that if x1, x2,..., xm , (m finite) are points of Rn and if some then ∃μ∈Ω with at most n+1 nonzero components and for which (See [5]). The authors of [2] have extended this result to include the case where m= +∞. In theorems 1 and 2 below we establish somewhat similar results for the case in which Ω is further restricted by a finite system of linear inequalities (or equalities). 
Cook, W. D. Carathéodory’s Theorem with Linear Constraints. Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 189-191. doi: 10.4153/CMB-1974-038-0
@article{10_4153_CMB_1974_038_0,
     author = {Cook, W. D.},
     title = {Carath\'eodory{\textquoteright}s {Theorem} with {Linear} {Constraints}},
     journal = {Canadian mathematical bulletin},
     pages = {189--191},
     year = {1974},
     volume = {17},
     number = {2},
     doi = {10.4153/CMB-1974-038-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-038-0/}
}
TY  - JOUR
AU  - Cook, W. D.
TI  - Carathéodory’s Theorem with Linear Constraints
JO  - Canadian mathematical bulletin
PY  - 1974
SP  - 189
EP  - 191
VL  - 17
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-038-0/
DO  - 10.4153/CMB-1974-038-0
ID  - 10_4153_CMB_1974_038_0
ER  - 
%0 Journal Article
%A Cook, W. D.
%T Carathéodory’s Theorem with Linear Constraints
%J Canadian mathematical bulletin
%D 1974
%P 189-191
%V 17
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-038-0/
%R 10.4153/CMB-1974-038-0
%F 10_4153_CMB_1974_038_0

[1] 1. Charnes, A., Cooper, W. W. and Kortanek, K., “Duality in semi-infinite programmes and some works of Haar and Carathéodory”, Man. Sci. 9 (1963), 209-228. Google Scholar

[2] 2. Cook, W. D. and Webster, R. J., “Carathéodorfs theorem”, Canadian Math. Bull. 15 (1972), 888. Google Scholar

[3] 3. Haar, A., “Uber Linear Ungleichungen”, Acta. Math. 2 (1924), 1-14. Google Scholar

[4] 4. Hadley, G., Linear programming, Addison-Wesley, Reading, Mass. (1962). Google Scholar

[5] 5. Reay, J. R., Generalizations of a theorem of Carathéodory, Memoirs Amer. Math. Soc. 54 (1965). Google Scholar

Cité par Sources :