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

作者：Wu Z Y^*; Quan J; Li G Q; Tian J

来源：Journal of Optimization Theory and Applications, 2012, 153(2): 408-435.

DOI：10.1007/s10957-011-9961-9

• Necessary local optimality conditions
• Necessary global optimality conditions
• Cubic polynomial optimization problem
• Local optimization methods
• Global optimization methods

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.

• 出版日期2012-5
• 单位宜宾学院; 上海大学