| 双层线性规划的一个全局优化方法 |
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| 引用本文： | 赵茂先,高自友.双层线性规划的一个全局优化方法[J].运筹学学报,2005,9(2):57-62. |
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| 作者姓名： | 赵茂先 高自友 |
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| 作者单位： | 1. 北京交通大学交通运输学院,北京,100044;山东科技大学应用数学系,青岛,266510
2. 北京交通大学交通运输学院,北京,100044 |
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| 基金项目： | This paper was partly supported by National Outstanding Young Investigator Grant (70225005) of National Natural Science Foundation of China and Teaching & Research Award Program for Outstanding Young Teachers (2001) in Higher Education Institutions of Ministry of Education, China. |
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| 摘 要： | 用线性规划对偶理论分析了双层线性规划的最优解与下层问题的对偶问题可行域上极点之间的关系，通过求得下层问题的对偶问题可行域上的极点，将双层线性规划转化为有限个线性规划问题，从而用线性规划方法求得问题的全局最优解．由于下层对偶问题可行域上只有有限个极点，所以方法具有全局收敛性．
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| 关 键 词： | 全局优化方法 对偶问题 线性规划问题 线性规划方法 全局最优解 全局收敛性 可行域 对偶理论 极点 有限 |
A Globally Convergent Algorithm for Solving the Bilevel Linear Programming Problem |
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| Zhao Maoxian,Gao Ziyou.A Globally Convergent Algorithm for Solving the Bilevel Linear Programming Problem[J].OR Transactions,2005,9(2):57-62. |
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| Authors: | Zhao Maoxian Gao Ziyou |
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| Institution: | Zhao Maoxian Gao Ziyou School of Traffic and Transportation,Beijing Jiaotong University,Beijing 100044,China, Department of Applied Mathematics,Shandong University of Science and Technology,Qingdao 266510,China |
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| Abstract: | In this paper, the relationship between the optimal solution of the bilevel linear programming problem and the extreme points of the feasible region of the follower's dual problem is discussed using the duality theory of linear program. This relationship leads to the decomposition of the composite problem into a series of linear programming problems leading to an efficient algorithm. The proposed algorithm can terminate at a global optimal solution to the problem in finite number of steps. Finally, a simple numerical example is given to illustrate the application of the algorithm. |
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| Keywords: | Operations research bilevel linear programming dual problem extreme point global convergence |
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