Volume 1,Issue 2
Fall 2025
混料信息矩阵的方向导数及改进的 Fedorov算法
为了构造复杂混料系统下搜索最优设计的算法，根据连续型设计的信息矩阵在单点设计方向的导数确定算法的迭代过程，通过分析单点设计方向上的 Fréchet导数与 Gâteaux导数的性质，构建改进的 Fedorov算法，进而提高搜索的效率。
[1]Scheffé H(1958).Experiments with Mixtures. Journal of the Royal Statistical Society(2), 344-360.
[2]Karunanithi A T, Achenie L E K, Gani R(2004).Optimal (Solvent) mixture design through a decomposition based CAMD methodology. Computer Aided Chemical
Engineering(04), 217-222.
[3]Limmun W, Borkowski J J, Chomtee B(2012).Using a genetic algorithm to generate D-optimal designs for mixture experiments. Quality and Reliability Engineering
International(7), 1055-1068.
[4]李光辉，张崇岐 (2017).具有复杂约束混料试验的渐近 D-最优设计．应用概率统计 (02), 203-220.
[5]Li G H, Zhang C Q.Random search algorithm for optimal mixture experimental design. Communication in Statistics: Theory and Methods(6), 1413-1422.
[6]Kiefer J. Optimum designs in regression problems, II［J］．The Annals of Mathematical Statistics, 1961, 32(1): 298-325.
[7]Gene H, Charles F. Matrix Computations-4th Edition［M］．The Johns Hopkins University Press,2023.
[8]李光辉，朱志彬，李俊鹏，等．混料试验的格点填充设计［J］．应用数学学报，2022,45(04):607-623.
[9]李光辉，李俊鹏，张崇岐．复杂约束域内混料最优设计的格点评价［J］．应用概率统计，2022,38(02):253-266.