关于二层规划最优解新定义的几点注解(英文)  

Some Notes on the Definition of Bilevel Programming Solution

作　　者：吕一兵[1] 胡铁松[1] 万仲平[2] 王广民[1] 

机构地区：[1]武汉大学系统工程研究所,武汉430072 [2]武汉大学数学与统计学院,武汉430072

出　　处：《运筹学学报》2007年第4期52-58,共7页Operations Research Transactions

基　　金：Supported by the National Nature Science Foundation of China(70371032, 50479039 and 70771080).

摘　　要：文献[2]提出了二层规划解的新定义,同时指出新定义能够解决更广泛的线性二层规划问题,并且如果线性二层规划的约束域为非空紧集,那么线性二层规划问题就存在Pareto最优解.本文用两个线性二层规划的例子说明文献[2]得出的结论是不可靠的,同时还分析了两种定义下的线性二层规划诱导域之间的关系.In reference [2], Shi Chenggen gave a new definition of linear bilevel programming （BLP） solution, and drawn the conclusions that the new definition could solve a wider class of problems, and if the constraint region of a linear BLP is nonempty and compact, then there exists a Pareto optimal solution for the linear BLP problem. However, in this paper, two counter-examples show that the above conclusions are not credible, then the relationship between the two kinds of inducible regions of the linear BLP is analyzed.

关 键 词：运筹学 线性二层规划 诱导域 最优解 

分 类 号：O221.1[理学—运筹学与控制论] TP301.6[理学—数学]