一类极大极小随机规划逼近问题最优解集的上半收敛性  

Upper Semi-Convergence of Optimal Solution Set for a Class of Minimax Stochastic Programming Approximation Problems

作　　者：霍永亮[1] 

机构地区：[1]重庆文理学院数学与财经学院数学研究所,重庆402160

出　　处：《应用数学》2016年第2期325-330,共6页Mathematica Applicata

基　　金：重庆高校创新团队建设计划项目(KJTD201321);重庆市群与图在决策中的应用重点实验室项目

摘　　要：本文首先将极大极小随机规划等价的转化为一个二层随机规划,在下层初始随机规划最优解集为多点集的情形下,给出下层随机规划逼近问题最优解集集值映射关于上层决策变量参数的上半收敛性和最优值函数的连续性.然后将上层随机规划等价转化为以上层和下层决策变量作为整体决策变量,以下层规划最优解集的图作为约束条件的单层规划,并在下层初始随机规划最优解集的图为正则的条件下,得到上层随机规划逼近问题最优解集关于最小信息概率度量收敛的上半收敛性.In this paper the author transforms minimax stochastic programming problems into equivalent bilevel stochastic programming problems.Suppose that optimal solution set of original lower level stochastic programming is multiple values set,we show continuity of optimal value and upper semiconvergence of the optimal solution set on the upper level decision variables of lower level stochastic programming approximation problem.Furthermore,we transform upper level stochastic programming problems into equivalent one-level stochastic programming problems,which are both upper and lower level decision variables as their global decision variables and graph of optimal solution sets of lower level stochastic programming as their constraint conditions.Under regularity conditions of graph of optimal solution sets for lower level original stochastic programming,we obtain the upper semi-convergence of optimal solution set of upper level stochastic programming.

关 键 词：极大极小随机规划 最优解集的图 最小信息概率度量 上半收敛性 

分 类 号：O221.6[理学—运筹学与控制论]