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

Z. Y. Wu (), J. Quan (), G. Q. Li () and J. Tian ()
Additional contact information
Z. Y. Wu: University of Ballarat
J. Quan: Yibin University
G. Q. Li: Shanghai University
J. Tian: University of Ballarat

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 2, No 10, 408-435

Abstract: 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.

Keywords: Necessary local optimality conditions; Necessary global optimality conditions; Cubic polynomial optimization problem; Local optimization methods; Global optimization methods (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-011-9961-9

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