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    block this user An-Ping Li

    Research Fellow

    Beijing 100085, P.R.China

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

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    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 derivatives. 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. Key words: Vector optimization, convex operator, directional derivative, decrease direction, normal cone, AMS Subject Classification: 90C29, 90C48 2 1. Introduction In optimization theory it is well known that convex functions as well as convex sets in play an important role. Convexity assumptions lead to significantly stronger reults than hold ...

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    Title : Convex Operators in Vector Optimization: Directional Derivatives and the Cone of Decrease Directions
    Abstract : 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 derivatives. 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. Key words: Vector optimization, convex operator, directional derivative, decrease direction, normal cone, AMS Subject Classification: 90C29, 90C48 2 1. Introduction In optimization theory it is well known that convex functions as well as convex sets in play an important role. Convexity assumptions lead to significantly stronger reults than hold ...
    Subject : unspecified
    Area : Mathematics
    Language : English
    Affiliations
    Url : http://kbibmp3.ub.uni-kl.de/Preprint/PS/report_40.ps.gz
    Doi : 10.1.1.51.8098

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    An-Ping's Peer Evaluation activity

    Emailed by 1
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    Downloads 761
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