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    A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere

    Access Status
    Fulltext not available
    Authors
    Wang, Y.
    Zhou, Guanglu
    Date
    2017
    Type
    Journal Article
    
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    Citation
    Wang, Y. and Zhou, G. 2017. A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere. Journal of the Operations Research Society of China. 5 (1): pp. 99-109.
    Source Title
    Journal of the Operations Research Society of China
    DOI
    10.1007/s40305-016-0148-9
    ISSN
    2194-668X
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/52420
    Collection
    • Curtin Research Publications
    Abstract

    © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.In this paper, we propose a hybrid second-order method for homogenous polynomial optimization over the unit sphere in which the new iterate is generated by employing the second-order information of the objective function. To guarantee the convergence, we recall the shifted power method when the second-order method does not make an improvement to the objective function. As the Hessian of the objective function can easily be computed and no line search is involved in the second-order iterative step, the method is not time-consuming. Further, the new iterate is generated in a relatively larger region and thus the global maximum can be likely obtained. The given numerical experiments show the efficiency of the proposed method.

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