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| 非线性-线性二层规划问题的罚函数方法 | |
| 引用本文： | 吕一兵,陈忠,万仲平,王广民.非线性-线性二层规划问题的罚函数方法[J].系统科学与数学,2009,29(5):630-636. |
| 作者姓名： | 吕一兵 陈忠 万仲平 王广民 |
| 作者单位： | 1. 长江大学信息与数学学院,荆州,434023 2. 武汉大学数学与统计学院,武汉,430072 3. 中国地质大学管理学院,武汉,430074 |
| 基金项目： | 国家自然科学基金，教育部重点实验室开放基金，长江大学博士科研启动基金 |
| 摘 要： | 利用下层问题的K-T最优性条件将下层为线性规划的一类非线性二层规划转化成相应的单层规划,同时取下层问题的互补条件为罚项,构造了该类非线性二层规划的罚问题.通过对相应罚问题性质的分析,得到了该类非线性二层规划问题的最优性条件,同时设计了该类二层规划问题的求解方法.数值结果表明该方法是可行、有效的. |
| 关 键 词： | 非线性二层规划 非线性规划 K-T条件 罚函数. |
| 收稿时间： | 2007-9-12 |
| 修稿时间： | 2008-8-6 |
A Penalty Function Method for Solving Nonlinear-Linear Bilevel Programming Problem |
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| L Yibing,CHEN Zhong,WAN Zhongping,WANG Guangmin.A Penalty Function Method for Solving Nonlinear-Linear Bilevel Programming Problem[J].Journal of Systems Science and Mathematical Sciences,2009,29(5):630-636. | |
| Authors: | L Yibing CHEN Zhong WAN Zhongping WANG Guangmin |
| Institution: | (1)School of Information and Mathematics, Yangtze University, Jingzhou 434023; (2)School of Mathematics and Statistics, Wuhan University, Wuhan 430072; (3)School of Management, China University of Geosciences, Wuhan 430074. |
| Abstract: | By using the Kuhn-Tucker optimality condition of the lower level problem, a class of nonlinear bilevel programming problem, whose lower level problem is linear programming problem, is transformed into a corresponding single level programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty. Throughanalyzing the properties of the penalized problem, the optimality condition of the nonlinear bilevel programming problem is given and an algorithm to solve it is proposed. The numerical result shows that the algorithm is feasible and efficient. |
| Keywords: | Nonlinear bilevel programming nonlinear programming Kuhn-Tucker condition penalty function |
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