TY - INPR
A1 - Topchishvili, Alexander L.
A1 - Maisuradze, Vilhelm G.
A1 - Ehrgott, Matthias
T1 - Convex Operators in Vector Optimization: Directional Derivatives and the Cone of Decrease Directions
N2 - The paper is devoted to the investigation of directional derivatives and the cone of decrease directions for convex operators on Banach spaces. We prove a condition for the existence of directional derivatives which does not assume regularity of the ordering cone K. This result is then used to prove that for continuous convex operators the cone of decrease directions can be represented in terms of the directional derivatices . Decrease directions are those for which the directional derivative lies in the negative interior of the ordering cone K. Finally, we show that the continuity of the convex operator can be replaced by its K-boundedness.
T3 - Report in Wirtschaftsmathematik (WIMA Report) - 40
KW - Vetor optimization
KW - convex operator
KW - directional derivative
KW - decrease direction
KW - normal cone
Y1 - 1999
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/514
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-4830
ER -