Convex Operators in Vector Optimization: Directional Derivatives and the Cone of Decrease Directions

  • 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.

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Author:Alexander L. Topchishvili, Vilhelm G. Maisuradze, Matthias Ehrgott
URN (permanent link):urn:nbn:de:hbz:386-kluedo-4830
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (40)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Tag:Vetor optimization ; convex operator ; decrease direction ; directional derivative ; normal cone
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):90C29 Multi-objective and goal programming
90C48 Programming in abstract spaces

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