线性约束三次规划问题的全局最优性必要条件和最优化算法  

Necessary global optimality conditions and optimization methods for cubic polynomial optimization problems with linear constraints

作　　者：叶敏[1] 吴至友[1] 张亮[1] 

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《运筹学学报》2015年第2期15-28,共14页Operations Research Transactions

基　　金：国家自然科学基金(No.NSFC11471062);重庆市自然科学基金(Nos.cstc2013jjB00001;cstc2011jjA00010)

摘　　要：讨论了带线性不等式约束三次规划问题的最优性条件和最优化算法.首先,讨论了带有线性不等式约束三次规划问题的全局最优性必要条件.然后,利用全局最优性必要条件,设计了解线性约束三次规划问题的一个新的局部最优化算法(强局部最优化算法).再利用辅助函数和所给出的新的局部最优化算法,设计了带有线性不等式约束三次规划问题的全局最优化算法.最后,数值算例说明给出的最优化算法是可行的、有效的.In this paper, the global optimality conditions and optimization methods for cubic polynomial optimization problems with linear inequality constraints are consid- ered. Firstly, we propose a necessary global optimality condition for cubic polynomial optimization problems with linear inequality constraints. Then, a new local optimization method （or called strongly local optimization methods） is presented by using its neces- sary global optimality conditions. A global optimization method is proposed for cubic polynomial optimization problems with linear inequality constraints by combining the new local optimization methods together with some auxiliary functions. Finally, some numerical examples are given to illustrate that these approaches are efficient.

关 键 词：三次规划问题 线性不等式约束 全局最优性必要条件 强局部优化算法 全局最优化算法 

分 类 号：O221.4[理学—运筹学与控制论]