混料试验渐近D-最优设计的聚类算法  

Asymptotically D-optimal Design of Mixture Experiment Using Clustering Algorithm

作　　者：罗嘉成 张崇岐 LUO Jia-cheng;ZHANG Chong-qi(School of Economics and Statistics,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学经济与统计学院,广东广州510006

出　　处：《数理统计与管理》2022年第3期402-412,共11页Journal of Applied Statistics and Management

基　　金：国家自然科学基金(12071096)。

摘　　要：由于混料试验设计的试验域或模型的复杂程度不同,在计算D-最优设计时,一般很难得到解析解。而常用的Fedorov算法,乘子算法以及其他的改进算法因为计算量大,灵活性不高等原因应用起来并不方便,本文提出一种计算混料试验渐近D-最优设计的聚类算法并证明了其收敛性。通过实例验证,该方法不仅能处理正规单纯形上的D-最优设计问题,对于复杂约束下的情况同样有效,与其他算法相比,该算法具有快速收敛的特性。Because of the complexity of the experimental design area or model of mixture design,it is difficult to get the analytical solution when calculating D-optimal design.The commonly used Fedorov algorithm,multiplicative algorithm and other improved algorithms are not convenient for application due to the large amount of computation and low flexibility,this paper presents a clustering algorithm to calculate the asymptotically D-optimal design of mixture experiment and the convergence is proved.Several examples show that this method can not only deal with D-optimal design on simplex area,but also be effective for complex constraints.Compared with other algorit hms,this algorithm can converge to D-optimal design fast.

关 键 词：混料试验设计 D-最优设计 Fedorov算法 乘子算法 

分 类 号：O212.6[理学—概率论与数理统计]