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    On the triality theory for a quartic polynomial optimization problem

    Access Status
    Open access via publisher
    Authors
    Gao, D.
    Wu, Changzhi
    Date
    2012
    Type
    Journal Article
    
    Metadata
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    Citation
    Gao, D. and Wu, C. 2012. On the triality theory for a quartic polynomial optimization problem. Journal of Industrial and Management Optimization. 8 (1): pp. 229-242.
    Source Title
    Journal of Industrial and Management Optimization
    DOI
    10.3934/jimo.2012.8.229
    ISSN
    1547-5816
    School
    Department of Construction Management
    URI
    http://hdl.handle.net/20.500.11937/39610
    Collection
    • Curtin Research Publications
    Abstract

    This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality. Results show that the triality theory holds strongly in the tri-duality form for our problem if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Some numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the local minimum and local maximum.

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