Geodesic
Partial Convexity
Matematičeskie zametki, Tome 75 (2004) no. 2, pp. 222-235

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

We study $OC$-convexity, which is defined by the intersection of conic semispaces of partial convexity. We investigate an optimization problem for $OC$-convex sets and prove a Krein–Milman type theorem for $OC$-convexity. The relationship between $OC$-convex and functionally convex sets is studied. Topological and numerical aspects, as well as separability properties are described. An upper estimate for the Carathéodory number for $OC$-convexity is found. On the other hand, it happens that the Helly and the Radon number for $OC$-convexity are infinite. We prove that the $OC$-convex hull of any finite set of points is the union of finitely many polyhedra. 
@article{MZM_2004_75_2_a5,
     author = {V. G. Naidenko},
     title = {Partial {Convexity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {222--235},
     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a5/}
}
TY  - JOUR
AU  - V. G. Naidenko
TI  - Partial Convexity
JO  - Matematičeskie zametki
PY  - 2004
SP  - 222
EP  - 235
VL  - 75
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a5/
LA  - ru
ID  - MZM_2004_75_2_a5
ER  - 
%0 Journal Article
%A V. G. Naidenko
%T Partial Convexity
%J Matematičeskie zametki
%D 2004
%P 222-235
%V 75
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a5/
%G ru
%F MZM_2004_75_2_a5
V. G. Naidenko. Partial Convexity. Matematičeskie zametki, Tome 75 (2004) no. 2, pp. 222-235. http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a5/