非线性-线性二层规划问题的罚函数方法

吕一兵;陈忠;万仲平;王广民

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (5) : 630-636.

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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (5) : 630-636. DOI: 10.12341/jssms08401
论文

非线性-线性二层规划问题的罚函数方法

    吕一兵(1), 陈忠(1), 万仲平(2), 王广民(3)
作者信息 +

A Penalty Function Method for Solving Nonlinear-Linear Bilevel Programming Problem

    LV Yibing(1), CHEN Zhong(1), WAN Zhongping(2), WANG Guangmin(3)
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摘要

利用下层问题的~K-T~最优性条件将下层为线性规划的一类非线性二层规划转化成相应的单层规划,同时取下层问题的互补条件为罚项,构造了该类非线性二层规划的罚问题. 通过对相应罚问题性质的分析,得到了该类非线性二层规划问题的最优性条件,同时设计了该类二层规划问题的求解方法.数值结果表明该方法是可行、有效的.

Abstract

By using the Kuhn-Tucker optimality condition of the lower level problem, a class of nonlinear bilevel programming problem, whose lower level problem is linear programming problem, is transformed into a corresponding single level programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty. Through
analyzing the properties of the penalized problem, the optimality condition of the nonlinear bilevel programming problem is given and an algorithm to solve it is proposed. The numerical result shows that the algorithm is feasible and efficient.

关键词

非线性二层规划 / 非线性规划 / K-T~条件 / 罚函数.

Key words

Nonlinear bilevel programming / nonlinear programming / Kuhn-Tucker condition / penalty function.

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吕一兵 , 陈忠 , 万仲平 , 王广民. 非线性-线性二层规划问题的罚函数方法. 系统科学与数学, 2009, 29(5): 630-636. https://doi.org/10.12341/jssms08401
LV Yibing , CHEN Zhong , WAN Zhongping , WANG Guangmin. A Penalty Function Method for Solving Nonlinear-Linear Bilevel Programming Problem. Journal of Systems Science and Mathematical Sciences, 2009, 29(5): 630-636 https://doi.org/10.12341/jssms08401
中图分类号： 90C05    90C26   
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