线性半向量二层规划问题的全局优化方法

doi:10.15960/j.cnki.issn.1007-6093.2015.02.003

运筹学学报 ›› 2015, Vol. 19 ›› Issue (2): 29-36.doi: 10.15960/j.cnki.issn.1007-6093.2015.02.003

线性半向量二层规划问题的全局优化方法

吕一兵^1,*, 万仲平²

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, 武汉 430072

收稿日期:2014-08-29 出版日期:2015-06-15 发布日期:2015-06-15
通讯作者: 吕一兵 lvyibing2001@gmail.com
基金资助:
国家自然科学基金(Nos. 11201039, 71171150, 61273179)

A global optimization method for solving the linear semivectorial bilevel programming problem

LV Yibing^1,*, WAN Zhongping²

1. School of Information and Mathematics, Yangtze University, Jingzhou 434023, Hubei, China; 2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2014-08-29 Online:2015-06-15 Published:2015-06-15

摘要/Abstract

摘要：

研究了线性半向量二层规划问题的全局优化方法. 利用下层问题的对偶间隙构造了线性半向量二层规划问题的罚问题, 通过分析原问题的最优解与罚问题可行域顶点之间的关系, 将线性半向量二层规划问题转化为有限个线性规划问题, 从而得到线性半向量二层规划问题的全局最优解. 数值结果表明所设计的全局优化方法对线性半向量二层规划问题是可行的.

关键词: 半向量二层规划, 对偶, 罚函数, 全局最优解

Abstract:

In this paper, we are concerned with global optimization approach for solving the linear semivectorial bilevel programming (LSBP) problem. Using the duality gap of the lower level programs, we construct the corresponding penalized problem. By analyzing the relationships between the optimal solutions of the original problem and the vertices of the feasible region of the penalized problem, we transform the LSBP problem to a series of linear programming problems. Then, the global optimal solution of the LSBP problem can be obtained by solving a series of linear programming problems. The numerical results show that the algorithm proposed is feasible to the LSBP problem.

Key words: semivectorial bilevel programming, duality, penalty function, global optimization solution

吕一兵, 万仲平. 线性半向量二层规划问题的全局优化方法[J]. 运筹学学报, 2015, 19(2): 29-36.

LV Yibing, WAN Zhongping. A global optimization method for solving the linear semivectorial bilevel programming problem[J]. Operations Research Transactions, 2015, 19(2): 29-36.

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线性半向量二层规划问题的全局优化方法

A global optimization method for solving the linear semivectorial bilevel programming problem

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