一类双层规划问题及其在矩阵对策中的应用  

A Bilevel Programming and Its Application in the Matrix Games

作　　者：白国仲[1] 

机构地区：[1]广东商学院数学系,广州510320

出　　处：《数学的实践与认识》2007年第24期124-131,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金资助项目(10571071)

摘　　要：基于建设节约型社会和保护资源环境的需要,提出了一类特殊的双层规划问题,即B规划.给出了B规划的数学模型、有关理论和求解方法.最后还给出了B规划在矩阵对策中的一个应用.我们把局中人设有得失控制值的对策问题称为稳妥型对策.稳妥型矩阵对策可化为B规划问题求解.Based on the demands of constructing a saving society, protecting natural environment and resources, a new bilevel programming problem is posed. It is said to be the B- Programming problem. This paper establishes the mathematical model of the B-programming problem, theory and solution. Lastly, an application of the B-programming in the matrix games is given. A game problem, in which every player has a controlled value of the gain and loss, is said to be a reliable game problem. A reliable matrix game may be transformed into a B- programming problem.

关 键 词：节约型社会 双层规划 数学模型 控制值 稳妥型矩阵对策 

分 类 号：O221[理学—运筹学与控制论] O225[理学—数学]