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二(双)层规划综述
引用本文:王广民,万仲平,王先甲.二(双)层规划综述[J].数学进展,2007,36(5):513-529.
作者姓名:王广民  万仲平  王先甲
作者单位:1. 中国地质大学管理学院,武汉,湖北,430074
2. 武汉大学数学与统计学院,武汉,湖北,430072
3. 武汉大学系统工程研究所,武汉,湖北,430072
摘    要:二(双)层规划是研究二层决策的递阶优化问题.其理论、方法和应用在过去的30多年取得了很大的发展.本文对二层规划问题的基本概念、性质和算法作了综述,并且对下层规划问题的解不唯一的情况也作了介绍,最后还给出了几种常见的二层规划模型.

关 键 词:二层规划  多层规划  最优性条件  Stackelberg问题  双线性规划  广义半无限规划
文章编号:1000-0917(2007)05-0513-17
修稿时间:2006-04-12

Bibliography on Bilevel Programming
WANG Guangmin,WAN Zhongping,WANG Xianjia.Bibliography on Bilevel Programming[J].Advances in Mathematics,2007,36(5):513-529.
Authors:WANG Guangmin  WAN Zhongping  WANG Xianjia
Institution:1. School of Management, China University of Geosciences, Wuhan, Hubei, 430074, P, R. China; 2. School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, 430072, P. R. China; 3. Institute of Systems Engineering, Wuhan University, Wuhan, Hubei, 430072, P. R. China
Abstract:The bilevel programming is hierarchical optimization on bilevel decision.The bilevel programming has been developed in its theory,algorithms and applications in the past more than 30 years.This paper overviews the bilevel programming problem from the sides of its basic definitions,nature,algorithms,and introduces the situation that the solution to the lower level programming problem is not unique.Finally,we also introduce some kinds of bilevel programming models.
Keywords:bilevel programming  multilevel  optimality condition  Stackelberg problem  bilinear programming  generalized semi-infinite programming
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