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    Semivectorial Bilevel Optimization on Riemannian Manifolds

    Access Status
    Fulltext not available
    Authors
    Bonnel, Henri
    Todjihoundé, L.
    Udriste, C.
    Date
    2015
    Type
    Journal Article
    
    Metadata
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    Citation
    Bonnel, H. and Todjihoundé, L. and Udriste, C. 2015. Semivectorial Bilevel Optimization on Riemannian Manifolds. Journal of Optimization Theory and Applications. 167 (2): pp. 464-486.
    Source Title
    Journal of Optimization Theory and Applications
    DOI
    10.1007/s10957-015-0789-6
    ISSN
    0022-3239
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/26233
    Collection
    • Curtin Research Publications
    Abstract

    © 2015, Springer Science+Business Media New York. In this paper, we deal with the semivectorial bilevel problem in the Riemannian setting. The upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multiobjective optimization problem to be solved by several followers acting in a cooperative way inside the greatest coalition and choosing among Pareto solutions with respect to a given ordering cone. For the so-called optimistic problem, when the followers choice among their best responses is the most favorable for the leader, we give optimality conditions. Also for the so-called pessimistic problem, when there is no cooperation between the leader and the followers, and the followers choice may be the worst for the leader, we present an existence result.

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