辽宁师范大学学报（自然科学版）
遼寧師範大學學報（自然科學版）
료녕사범대학학보（자연과학판）
JOURNAL OF LIAONING NORMAL UNIVERSITY(NATURAL SCIENCE)
2014年
2期
153-156
,共4页
任咏红%王佳%王榆%马艳妮
任詠紅%王佳%王榆%馬豔妮
임영홍%왕가%왕유%마염니
样本均值近似%机会约束%Log-Sigmoid近似
樣本均值近似%機會約束%Log-Sigmoid近似
양본균치근사%궤회약속%Log-Sigmoid근사
sample average approximation%chance constraints%Log-Sigmoid approximation
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。
樣本均值近似（SAA）方法在機會約束優化問題中扮縯著重要的角色。基于機會約束優化問題的Log-Sigmoid近似，探討求解Log-Sigmoid近似問題的樣本均值近似方法。構造瞭約束函數的樣本均值近似函數，建立瞭相應的樣本均值近似問題，併且證明噹樣本數量足夠大時，樣本均值近似問題的最優值和最優解集分彆以概率為1收斂于Log-Sigmoid近似問題的最優值和最優解集。
양본균치근사（SAA）방법재궤회약속우화문제중분연착중요적각색。기우궤회약속우화문제적Log-Sigmoid근사，탐토구해Log-Sigmoid근사문제적양본균치근사방법。구조료약속함수적양본균치근사함수，건립료상응적양본균치근사문제，병차증명당양본수량족구대시，양본균치근사문제적최우치화최우해집분별이개솔위1수렴우Log-Sigmoid근사문제적최우치화최우해집。
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 .
