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:nbn:de:hbz:386-kluedo-4830 Report in Wirtschaftsmathematik (WIMA Report) (40) Preprint English 1999 1999 Technische Universität Kaiserslautern 2000/04/03 Vetor optimization ; convex operator ; decrease direction ; directional derivative ; normal cone Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C29 Multi-objective and goal programming 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C48 Programming in abstract spaces Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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