多随从二层优化问题一个新的解概念及性质  

A new concept of bilevel programming problem with multiple followers and some properties

作　　者：杨龙宝[1] 杨丰梅[1] 

机构地区：[1]北京化工大学理学院,北京100029

出　　处：《北京化工大学学报（自然科学版）》2005年第2期81-84,共4页Journal of Beijing University of Chemical Technology(Natural Science Edition)

基　　金：国家自然科学基金(10171108)

摘　　要：文中讨论了多随从双层规划问题。根据对策论中Nash均衡点的思想和多目标决策中极大模理想点技术,给出了极大Nash理想点的定义,并对多随从双层规划问题引入了极大Nash最优解的概念。最优解概念不仅有效地解决了随从响应不唯一所带来的解的不确定性,而且利用变换可以将对应的问题转化为求解过程比较容易的数学模型。用不动点定理证明了极大Nash最优解的存在性,并证明了解集的闭性。A bilevel programming problem with multiple followers was concerned. Based on the concept of an equilibrium in Game Theory and the idea of Goal Programming, a Nash-ideal-point conception was introduced, and the new Nash conception for the problem was obtained. This is an efficient way to avoid the uncertainty caused by the multiple potential reactions. In the same time it may simplify the mathematical model. The existence of a solution is proven under some mild conditions. A property of the solution set was also discussed.

关 键 词：二层规划 多随从 Nash解 

分 类 号：O122[理学—数学]