Geodesic
Some Generalizations of Carathéodory′s Theorem Via Barycentres, with Application to Mathematical Programming
Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 339-346

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A theorem on the barycentre of a measure is proven which leads to generalization of Carathéodory′s theorem and to extension of various results. A mathematical programming problem is examined in application. 
Tijs, S. H.; Borwein, J. M. Some Generalizations of Carathéodory′s Theorem Via Barycentres, with Application to Mathematical Programming. Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 339-346. doi: 10.4153/CMB-1980-048-x
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     author = {Tijs, S. H. and Borwein, J. M.},
     title = {Some {Generalizations} of {Carath\'eodory's} {Theorem} {Via} {Barycentres,} with {Application} to {Mathematical} {Programming}},
     journal = {Canadian mathematical bulletin},
     pages = {339--346},
     year = {1980},
     volume = {23},
     number = {3},
     doi = {10.4153/CMB-1980-048-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-048-x/}
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