随机规划问题最优值的收敛性分析  

Convergence Analysis of the Optimal Value of Stochastic Programming

作　　者：刘晋纹 韩有攀[1] LIU Jinwen;HAN Youpan(School of Science,Xi’an Polytechnic University,Xi’an 710600,China)

机构地区：[1]西安工程大学理学院,西安710600

出　　处：《河南科学》2021年第6期861-867,共7页Henan Science

基　　金：国家自然科学基金资助项目(11501434)。

摘　　要：大偏差理论是研究随机问题渐进性的有效工具.在样本非独立同分布(i.i.d)条件下,对随机规划问题最优值的指数收敛性进行研究.对通常的随机规划问题在目标函数满足全局Lipschitz条件时,利用G?rtner-Ellis大偏差定理建立其最优值的指数收敛性.把类似的方法应用到极小极大随机规划问题中,给出了其最优值的指数收敛性.Large deviation theory is an effective tool to study asymptotic of stochastic problems.In this paper,the exponential convergence of the optimal value of stochastic programming is studied under the condition that the sample are not independent and identity distribution.For conventional stochastic programming problems,when the objective function satisfies the global Lipschitz condition,the exponential convergence of the optimal value is established by using the G?rtner-Ellis large deviation theorem.The similar method is applied to the minimax stochastic programming problem,and the exponential convergence of the optimal value is given.

关 键 词：随机规划问题 全局Lipschitz条件 G?rtner-Ellis大偏差定理 指数收敛 

分 类 号：O221.5[理学—运筹学与控制论]