Geodesic
From Linear to Convex Systems: Consistency, Farkas' Lemma and Applications
Journal of convex analysis, Tome 13 (2006) no. 1, pp. 113-133 
N. Dinh; M. A. Goberna; M. A. López. From Linear to Convex Systems: Consistency, Farkas' Lemma and Applications. Journal of convex analysis, Tome 13 (2006) no. 1, pp. 113-133. http://geodesic.mathdoc.fr/item/JCA_2006_13_1_JCA_2006_13_1_a7/
@article{JCA_2006_13_1_JCA_2006_13_1_a7,
     author = {N. Dinh and M. A. Goberna and M. A. L\'opez},
     title = {From {Linear} to {Convex} {Systems:} {Consistency,} {Farkas'} {Lemma} and {Applications}},
     journal = {Journal of convex analysis},
     pages = {113--133},
     year = {2006},
     volume = {13},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_1_JCA_2006_13_1_a7/}
}
TY  - JOUR
AU  - N. Dinh
AU  - M. A. Goberna
AU  - M. A. López
TI  - From Linear to Convex Systems: Consistency, Farkas' Lemma and Applications
JO  - Journal of convex analysis
PY  - 2006
SP  - 113
EP  - 133
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JCA_2006_13_1_JCA_2006_13_1_a7/
ID  - JCA_2006_13_1_JCA_2006_13_1_a7
ER  - 
%0 Journal Article
%A N. Dinh
%A M. A. Goberna
%A M. A. López
%T From Linear to Convex Systems: Consistency, Farkas' Lemma and Applications
%J Journal of convex analysis
%D 2006
%P 113-133
%V 13
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2006_13_1_JCA_2006_13_1_a7/
%F JCA_2006_13_1_JCA_2006_13_1_a7

Voir la notice de l'article provenant de la source Heldermann Verlag

This paper analyzes inequality systems with an arbitrary number of proper lower semicontinuous convex constraint functions and a closed convex constraint subset of a locally convex topological vector space. More in detail, starting from well-known results on linear systems (with no constraint set), the paper reviews and completes previous works on the above class of convex systems, providing consistency theorems, two new versions of Farkas' lemma, and optimality conditions in convex optimization. A new closed cone constraint qualification is proposed. Suitable counterparts of these results for cone-convex systems are also given.