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极大极小随机规划逼近问题最优解集和最优值的稳定性

霍永亮1,*   

  1. 1. 重庆文理学院数学研究所，重庆市群与图的理论及其应用重点实验室，重庆永川 402160
  • 收稿日期:2014-12-29 出版日期:2016-03-15 发布日期:2016-03-15
  • 通讯作者: 霍永亮 yongliang-huo@126.com
  • 基金资助:

    重庆高校创新团队建设计划项目(No. KJTD201321), 中国博士后科学基金资助项目(No. 2015M57016), 重庆市教委科学技术研究项目(No. KJ1500334)

Stability of optimal solution set and optimal value for minimax stochastic programming approximation problems

HUO Yongliang1,*   

  1. 1. Institute of Mathematics, Chongqing University of Arts and Sciences，Chongqing Key Lab. of Group & Graph Theories and Applications，Yongchuan  Chongqing  402160，China
  • Received:2014-12-29 Online:2016-03-15 Published:2016-03-15

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摘要：

研究了特殊的二层极大极小随机规划逼近收敛问题. 首先将下层初始随机规划最优解集拓展到非单点集情形, 且可行集正则的条件下, 讨论了下层随机规划逼近问题最优解集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. 然后把下层随机规划的epsilon-最优解向量函数反馈到上层随机规划的目标函数中, 得到了上层随机规划逼近问题的最优解集关于最小信息概率度量收敛的上半收敛性和最优值的连续性.

关键词: 极大极小随机规划, 正则条件, 最小信息概率度量, 最优解集, 上半收敛性

Abstract:

In this paper, we research convergence of minimax approximation problems  of special class of bilevel stochastic programming. First, under regularity conditions of feasible set, we expand optimal solution set of lower level original stochastic programming to into non-singleton set. And we give continuity of optimal value and upper semi-convergence of the optimal solution  set on the upper level decision variables for lower level stochastic programming approximation problem. Furthermore, we feedback $\varepsilon$-optimal solution vector function provided by the lower level stochastic programming into the objective function of the upper level stochastic programming problems, and obtain the continuity of optimal value and the upper semi-convergence of optimal solution set with respect to the minimal information (m.i.) probability metric for upper level programming.

Key words: minimax stochastic programming, regularity condition, minimal information (m.i.) probability metric, optimal solution set, upper semi-convergence