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    Differential properties and optimality conditions for generalized weak vector variational inequalities

    Access Status
    Fulltext not available
    Authors
    Zhu, S.
    Li, S.
    Teo, Kok Lay
    Date
    2013
    Type
    Journal Article
    
    Metadata
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    Citation
    Zhu, S. and Li, S. and Teo, K.L. 2013. Differential properties and optimality conditions for generalized weak vector variational inequalities. Positivity. 17 (3): pp. 443-457.
    Source Title
    Positivity
    DOI
    10.1007/s11117-012-0179-3
    ISSN
    1385-1292
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/45897
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we study a generalized weak vector variational inequality, which is a generalization of a weak vector variational inequality and a Minty weak vector variational inequality. By virtue of a contingent derivative and a Φ-contingent cone, we investigate differential properties of a class of set-valued maps and obtain an explicit expression of its contingent derivative. We also establish some necessary optimality conditions for solutions of the generalized weak vector variational inequality, which generalize the corresponding results in the literature. Furthermore, we establish some unified necessary and sufficient optimality conditions for local optimal solutions of the generalized weak vector variational inequality. Simultaneously, we also show that there is no gap between the necessary and sufficient conditions under an appropriate condition.

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