近似秩函数的一阶导数和二阶导数
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摘要
矩阵秩优化的光滑函数方法依赖矩阵秩的光滑近似.光滑函数方法涉及光滑近似秩函数的一、二阶导数.因此给出一个具体的近似秩函数的一、二阶导数的计算公式.
The smooth function method of the rank of matrix optimization depends on the smooth approximation of the rank of matrix and it involves the first or the second derivatives of the smoothing rank function.In this paper we give the first and second derivatives of a specific approximation rank function.
The smooth function method of the rank of matrix optimization depends on the smooth approximation of the rank of matrix and it involves the first or the second derivatives of the smoothing rank function.In this paper we give the first and second derivatives of a specific approximation rank function.
引文
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[2]乔熔岩,赵新国.改进共轭梯度法求解无约束二次凸规划问题[J].大学数学,2014,30(6):38-42.
[3]Hiriart-Urruty J B,Hai Y L.A variational approach of the rank function[J].TOP,2013,21(2):207-240.
[4]Magnus J R,Neudecker H.Matrix differential calculus with applications in statistics and econometrics[M].New York:Wiley,1988.
[5]Zhao Y B.An approximation theory of matrix rank minimization and its application to quadratic equations[J].Linear Algebra and Its Applications,2012,437(1):77-93.