| 求解半向量双层规划问题的精确罚函数法 |
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| 引用本文： | 任爱红,王宇平.求解半向量双层规划问题的精确罚函数法[J].系统工程理论与实践,2014,34(4):910-916. |
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| 作者姓名： | 任爱红 王宇平 |
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| 作者单位： | 1. 西安电子科技大学 计算机学院, 西安 710071;2. 宝鸡文理学院 数学系, 宝鸡 721013 |
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| 基金项目： | 国家自然科学基金(61272119,61203372);中央高校基本科研业务费(5051303009) |
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| 摘 要： | 研究半向量双层规划问题的求解方法. 利用Benson’s方法及线性规划问题的对偶理论，将半向量双层规划问题转化为一个单层优化问题，同时提出了转化问题的偏静态条件定义. 基于此定义，构造了半向量双层规划的精确罚问题，得到了此类双层规划问题的最优性条件，并给出相应的求解方法. 最后通过一个数值例子表明了求解方法的可行性.
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| 关 键 词： | 半向量双层规划 多目标规划 偏静态条件 罚函数法 |
| 收稿时间： | 2012-07-18 |
Exact penalty function method for solving semivectorial bilevel programming problem |
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| REN Ai-hong,WANG Yu-ping.Exact penalty function method for solving semivectorial bilevel programming problem[J].Systems Engineering —Theory & Practice,2014,34(4):910-916. |
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| Authors: | REN Ai-hong WANG Yu-ping |
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| Institution: | 1. School of Computer Science and Technology, Xidian University, Xi'an 710071, China;2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, China |
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| Abstract: | This paper considered the semivectorial bilevel programming problem. By using Benson's method and dual theory of linear programming, the original problem was transformed into a single level optimization problem. This paper gave a definition of partial calmness of the transformed problem. Based on this definition, this paper constructed an exact penalized problem of the semivectorial bilevel programming problem, gave its optimality condition, and proposed an algorithm to solve it. Finally, this paper gave a numerical example to show that the algorithm is feasible. |
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| Keywords: | semivectorial bilevel programming multi-objective programming partial calmness penalty method |
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