| 优化方法解决无上层约束的线性双层规划问题 |
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| 引用本文： | 邓键,黄庆道,马明娟.优化方法解决无上层约束的线性双层规划问题[J].东北数学,2008,24(5):433-446. |
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| 作者姓名： | 邓键 黄庆道 马明娟 |
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| 作者单位： | |
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| 基金项目： | 面向21世纪教育振兴行动计划（985计划） |
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| 摘 要： | In this paper we propose an optimal method for solving the linear bilevel programming problem with no upper-level constraint. The main idea of this method is that the initial point which is in the feasible region goes forward along the optimal direction firstly. When the iterative point reaches the boundary of the feasible region, it can continue to go forward along the suboptimal direction. The iteration is terminated until the iterative point cannot go forward along the suboptimal direction and effective direction, and the new iterative point is the solution of the lower-level programming. An algorithm which bases on the main idea above is presented and the solution obtained via this algorithm is proved to be optimal solution to the bilevel programming problem. This optimal method is effective for solving the linear bilevel programming problem.
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| 关 键 词： | 规划问题 线性 求解 优化 上限 迭代点 二层规划 可行域 |
An Optimal Method for Solving the Linear Bilevel Programming Problem with No Upper-level Constraint |
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| DENG Jian,HUANG Qing-dao,MA Ming-juan.An Optimal Method for Solving the Linear Bilevel Programming Problem with No Upper-level Constraint[J].Northeastern Mathematical Journal,2008,24(5):433-446. |
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| Authors: | DENG Jian HUANG Qing-dao MA Ming-juan |
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| Institution: | [1]Department of Mathematics, Jilin University, Changchun, 130012 [2]Foundation Department, China Aviation University of Air Force, Changchun, 130022 |
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| Abstract: | In this paper we propose an optimal method for solving the linear bilevel programming problem with no upper-level constraint.The main idea of this method is that the initial point which is in the feasible region goes forward along the opti-mal direction firstly.When the iterative point reaches the boundary of the feasible region, it can continue to go forward along the suboptimal direction.The iteration is terminated until the iterative point cannot go forward along the suboptimal direction and effective direction, and the new iterative point is the solution of the lower-level programming.An algorithm which bases on the main idea above is presented and the solution obtained via this algorithm is proved to be optimal solution to the bilevel programming problem.This optimal method is effective for solving the linear bilevel programming problem. |
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| Keywords: | bilevel optimal suboptimal |
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