English

运筹学学报 ›› 2015, Vol. 19 ›› Issue (2): 15-28.doi: 10.15960/j.cnki.issn.1007-6093.2015.02.002

• 运筹学 • 上一篇    下一篇

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

叶敏1, 吴至友1,*, 张亮1   

  1. 1. 重庆师范大学数学科学学院, 重庆 401331
  • 收稿日期:2014-05-28 出版日期:2015-06-15 发布日期:2015-06-15
  • 通讯作者: 吴至友 zywu@cqnu.edu.cn
  • 基金资助:

    国家自然科学基金(No. NSFC11471062), 重庆市自然科学基金(Nos. cstc2013jjB00001, cstc2011jjA00010)

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

YE Min1, WU Zhiyou1,*, ZHANG Liang1   

  1. 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
  • Received:2014-05-28 Online:2015-06-15 Published:2015-06-15

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1484

被引次数

2

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 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.

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

Abstract:

In this paper, the global optimality conditions and optimization methods for cubic polynomial optimization problems with linear inequality  constraints are considered. 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 necessary 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.

Key words: cubic polynomial optimization problems, linear inequality constraints, necessary global optimality condition, strongly local optimization method, global optimization method