| 一种求解线性二层规划的割平面方法 |
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| 引用本文： | 吕一兵,万仲平. 一种求解线性二层规划的割平面方法[J]. 数学的实践与认识, 2012, 42(21): 114-120 |
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| 作者姓名： | 吕一兵 万仲平 |
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| 作者单位： | 1. 长江大学信息与数学学院,湖北荆州,434023
2. 武汉大学数学与统计学院,湖北武汉,430072 |
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| 基金项目： | 国家自然科学基金，湖北省教育厅重点项目，长江大学博士基金 |
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| 摘 要： | 以下层问题的K-T最优性条件代替下层问题,将线性二层规划转化为相应的单层规划问题,通过分析单层规划可行解集合的结构特征,设计了一种求解线性二层规划全局最优解的割平面算法.数值结果表明所设计的割平面算法是可行、有效的.
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| 关 键 词： | 线性二层规划 K-T条件 割平面 全局最优解 |
A.Cutting Plane Algorithm for Solving Linear Bilevel Programs |
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| LV Yi-bing , WAN Zhong-ping. A.Cutting Plane Algorithm for Solving Linear Bilevel Programs[J]. Mathematics in Practice and Theory, 2012, 42(21): 114-120 |
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| Authors: | LV Yi-bing WAN Zhong-ping |
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| Affiliation: | 1.School of Information and Mathematics,Yangtze University,Jingzhou 434023,China) (2.School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China) |
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| Abstract: | Using the approach of replacing the lower level problem by its K-T optimality conditions,we transform the linear bilevel programs into the corresponding single level programs. Through analyzing the structural feature of the single level programs' feasible region, we propose a globally convergent cutting plane algorithm for the linear bilevel programming problem.Then,a numerical example is given to illustrate the algorithm. |
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| Keywords: | linear bilevel programming K-T optimality condition cutting plane global optimal solution |
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