求解机会约束优化的Log-Sigmoid近似问题的样本均值近似方法

Sample average approximation approach for Log-Sigmoid approximation of chance constrained problem

样本均值近似(SAA)方法在机会约束优化问题中扮演着重要的角色.基于机会约束优化问题的Log-Sigmoid近似,探讨求解Log-Sigmoid近似问题的样本均值近似方法.构造了约束函数的样本均值近似函数,建立了相应的样本均值近似问题,并且证明当样本数量足够大时,样本均值近似问题的最优值和最优解集分别以概率为1收敛于Log-Sigmoid近似问题的最优值和最优解集.

Sample average approximation （SAA） method plays an important role in chance constrained optimization problems . Based on Log-Sigmoid approximation of chance constrained optimization problem ,this paper aims at discussing the sample average approximation method for solving the Log-Sigmoid approximation problem .The sample average approximation function of constraint function is built ,and the corresponding sample average approximation problem is established .Moreover ,it proves that the optimal value and set of optimal solutions of the sample average approximation prob-lem converge to those of Log-Sigmoid approximation problem with probability 1 respectively when the sample size is large enough .