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    A smoothing scheme for optimization problems with max-min constraints

    Access Status
    Fulltext not available
    Authors
    Huang, X.
    Yang, X.
    Teo, Kok
    Date
    2007
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Huang, X. and Yang, X. and Teo, Kok Lay. 2007. A smoothing scheme for optimization problems with max-min constraints. Journal of Industrial and Management Optimization. 3 (2): pp. 209-222.
    Source Title
    Journal of Industrial and Management Optimization
    Additional URLs
    http://aimsciences.org/journals/pdfs.jsp?paperID=2259&mode=full
    ISSN
    15475816
    Faculty
    Department of Mathematics and Statistics
    School of Science
    Faculty of Science and Engineering
    Remarks

    The link to the journal’s home page is: http://aimsciences.org/journals/jimo/contents.jsp

    URI
    http://hdl.handle.net/20.500.11937/38706
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we apply a smoothing approach to a minimization problem with a max-min constraint (i.e., a min-max-min problem). More specifically, we first rewrite the min-max-min problem as an optimization problem with several min-constraints and then approximate each min-constraint function by a smooth function. As a result, the original min-max-min optimization problem can be solved by solving a sequence of smooth optimization problems. We investigate the relationship between the global optimal value and optimal solutions of the original min-max-min optimization problem and that of the approximate smooth problem. Under some conditions, we show that the limit points of the first-order (second-order) stationary points of the smooth optimization problems are first-order (second-order) stationary points of the original min-max-min optimization problem.

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