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    A new exact penalty method for semi-infinite programming problems

    196108_196108.pdf (319.7Kb)
    Access Status
    Open access
    Authors
    Lin, Qun
    Loxton, Ryan
    Teo, Kok Lay
    Wu, Yong Hong
    Yu, C.
    Date
    2014
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Lin, Qun and Loxton, Ryan and Teo, Kok Lay and Wu, Yong Hong and Yu, Changjun. 2014. A new exact penalty method for semi-infinite programming problems. Journal of Computational and Applied Mathematics. 261: pp. 271-286.
    Source Title
    Journal of Computational and Applied Mathematics
    DOI
    10.1016/j.cam.2013.11.010
    ISSN
    0377-0427
    Remarks

    NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, Vol. 261 (2014). DOI: 10.1016/j.cam.2013.11.010

    URI
    http://hdl.handle.net/20.500.11937/22707
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we consider a class of nonlinear semi-infinite optimization problems. These problems involve continuous inequality constraints that need to be satisfied at every point in an infinite index set, as well as conventional equality and inequality constraints. By introducing a novel penalty function to penalize constraint violations, we form an approximate optimization problem in which the penalty function is minimized subject to only bound constraints. We then show that this penalty function is exact—that is, when the penalty parameter is sufficiently large, any local solution of the approximate problem can be used to generate a corresponding local solution of the original problem. On this basis, the original problem can be solved as a sequence of approximate nonlinear programming problems. We conclude the paper with some numerical results demonstrating the applicability of our approach to PID control and filter design.

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