一类酉约束矩阵迹函数最大值问题的解析解  

Analytical solutions of a class of matrix trace maximization problems with unitary constraints

作　　者：余俊伟 陆明杰 徐玮玮[1] YU Jun-wei;LU Ming-jie;XU Wei-wei(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,Jiangsu,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《云南大学学报（自然科学版）》2022年第1期16-22,共7页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11971243);江苏省自然科学基金(BK20181405)。

摘　　要：酉约束的矩阵优化问题在数据控制理论和电子结构计算等领域内有着非常广泛的应用.考虑了一类酉约束的矩阵迹函数最大值问题:SkSk^(H)=In,WkWkH^(max)=It,VkVk^(H)=1m|tr(CIm±k=1П2ГkSk△kWkHkVk)|,其中Γk,Δk,Ηk分别是m×n,n×t,t×m复对角矩阵,k=1,2;c是复数,tr(·)表示矩阵迹函数,Im是m×m单位矩阵.在前人研究的基础上首先考虑了系数c是复数,所研究矩阵是不同维的情况,最后给出数值实验验证了所得结果的有效性.The matrix optimization problem with unitary constraints is widely used in the fields of data control theory and electronic structure calculation.In this paper,we consider a class of unitary constrained matrix trace maximization problems as follows:SkSk^(H)=In,WkWkH^(max)=It,VkVk^(H)=1m|tr(CIm±k=1П2ГkSk△kWkHkVk)|,where Γ;,Δ;,Η;, are m×n,n×t,t×m complex diagonal matrices respectively,k=1,2.c∈C,tr(·) denotes the matrix trace function,I;is the m×m identity matrix.On the basis of predecessor research result,it is considered that the coefficients are complex and the studied matrix is of different dimensions.Finally,numerical experiments are given to verify the effectiveness of the results.

关 键 词：酉约束 矩阵迹函数 解析解 

分 类 号：O241[理学—计算数学]