两种线性二层规划最优解定义的探讨

A discussion on the two kinds of definitions of linear bilevel programming solution

为了更好地解决上层带有任意线性约束形式的线性二层规划问题,Chenggen Shi提出了有关线性二层规划解的新定义。本文对Chenggen Shi提出的线性二层规划解的定义与原线性二层规划解的定义之间的关系进行了分析。给出的一个算例表明,对同一个线性二层规划问题,两种最优解定义有可能得到不同的结果,进而提出了两种线性二层规划最优解定义的等价性条件。

In order to well deal with a linear bilevel programming problem when the upper--level＇s constraint functions are of arbitrary linear form, Chenggen Shi gave a new definition of linear bilevel programming solution. This paper analyses the relationship between the new definition given by Chenggen Shi and the original definition of linear bilevel programming solution. A designed linear bilevel programming problem shows that under the two different definitions of linear bilevel programming solution, the same linear bilevel programming problem may have different optimal solutions. Then, this paper proposes the equivalent condition between the two kinds of definitions of linear hilevel programming solution. The example shows that the equivalent condition proposed above is correct.