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Necessary Optimality Conditions and New Optimization Methods for Cubic Polynomial Optimization Problems with Mixed Variables

Author

Listed:
  • Z. Y. Wu

    (University of Ballarat)

  • J. Quan

    (Yibin University)

  • G. Q. Li

    (Shanghai University)

  • J. Tian

    (University of Ballarat)

Abstract

Multivariate cubic polynomial optimization problems, as a special case of the general polynomial optimization, have a lot of practical applications in real world. In this paper, some necessary local optimality conditions and some necessary global optimality conditions for cubic polynomial optimization problems with mixed variables are established. Then some local optimization methods, including weakly local optimization methods for general problems with mixed variables and strongly local optimization methods for cubic polynomial optimization problems with mixed variables, are proposed by exploiting these necessary local optimality conditions and necessary global optimality conditions. A global optimization method is proposed for cubic polynomial optimization problems by combining these local optimization methods together with some auxiliary functions. Some numerical examples are also given to illustrate that these approaches are very efficient.

Suggested Citation

  • Z. Y. Wu & J. Quan & G. Q. Li & J. Tian, 2012. "Necessary Optimality Conditions and New Optimization Methods for Cubic Polynomial Optimization Problems with Mixed Variables," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 408-435, May.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:2:d:10.1007_s10957-011-9961-9
    DOI: 10.1007/s10957-011-9961-9
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    References listed on IDEAS

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    1. Hanoch, Giora & Levy, Haim, 1970. "Efficient Portfolio Selection with Quadratic and Cubic Utility," The Journal of Business, University of Chicago Press, vol. 43(2), pages 181-189, April.
    2. Yanjun Wang & Zhian Liang, 2010. "Global optimality conditions for cubic minimization problem with box or binary constraints," Journal of Global Optimization, Springer, vol. 47(4), pages 583-595, August.
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    Cited by:

    1. Wu, Zhiyou & Tian, Jing & Quan, Jing & Ugon, Julien, 2014. "Optimality conditions and optimization methods for quartic polynomial optimization," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 968-982.
    2. Z. Wu & J. Tian & J. Ugon, 2015. "Global optimality conditions and optimization methods for polynomial programming problems," Journal of Global Optimization, Springer, vol. 62(4), pages 617-641, August.

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