二层随机规划逼近ε-最优解集的Hausdorff收敛性  

The Hausdorff Convergence of the Optimal Solution Set of Approximation for Bi-Level Stochastic Programming

作　　者：周婉娜[1] 霍永亮[2] 胡之英[1] 

机构地区：[1]西安翻译学院基础课部大学数学教研室,中国西安710105 [2]重庆文理学院数学与财经学院数学研究所,中国重庆402160

出　　处：《湖南师范大学自然科学学报》2016年第3期80-83,共4页Journal of Natural Science of Hunan Normal University

基　　金：陕西省教育科学"十二五"规划2013年度课题(SGH13460)

摘　　要：二层随机规划是由上、下层随机规划组成的,下层随机规划是以上层决策变量为参数的随机规划问题,而上层是以下层随机规划的最优值作为响应的随机规划问题,对于此类的二层随机规划问题,本文首先讨论了下层随机规划最优值的收敛性,然后将下层随机规划的最优值反馈到上层,得到了上层随机规划逼近ε-最优解集序列的Hausdorff收敛性.Bi-level stochastic programming is through upper and lower levels of stochastic programming. The lower level stochastic programming uses the upper decision variables as the parameters of stochastic programming problems. The upper level stochastic programming is a stochastic programming problem including a parametric optimal value of the lower level stochastic programming. For the bi-level stochastic programming problem, this article first discusses the optimal value convergence of lower stochastic programming, and then feedback the optimal value of lower level stochastic programming to the upper level, obtaining the Hausdorff convergence of the upper level stochastic programming approximation optimal solution sequence.

关 键 词：二层随机规划 ε-最优解集 最优值 Hausdorff收敛性 

分 类 号：O221.5[理学—运筹学与控制论]