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Global optimality conditions and optimization methods for polynomial programming problems

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  • Z. Wu
  • J. Tian
  • J. Ugon

Abstract

This paper is concerned with the general polynomial programming problem with box constraints, including global optimality conditions and optimization methods. First, a necessary global optimality condition for a general polynomial programming problem with box constraints is given. Then we design a local optimization method by using the necessary global optimality condition to obtain some strongly or $$\varepsilon $$ ε -strongly local minimizers which substantially improve some KKT points. Finally, a global optimization method, by combining the new local optimization method and an auxiliary function, is designed. Numerical examples show that our methods are efficient and stable. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:4:p:617-641
    DOI: 10.1007/s10898-015-0292-5
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    References listed on IDEAS

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    1. 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.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. V. Jeyakumar & G. Li & S. Srisatkunarajah, 2014. "Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations," Journal of Global Optimization, Springer, vol. 58(1), pages 31-50, January.
    4. 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.
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    Cited by:

    1. Wang, Jianzhou & Dong, Yunxuan & Zhang, Kequan & Guo, Zhenhai, 2017. "A numerical model based on prior distribution fuzzy inference and neural networks," Renewable Energy, Elsevier, vol. 112(C), pages 486-497.

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