Optimization Notes

2016/8/30

学习ADMM（Alternating Direction Method of Multiplers）

ADMM是一个旨在将对偶上升法的可分解性和乘子法的上界收敛属性融合在一起的算法。

2016/9/23

矩阵求导示例：

Y = A * X --> DY/DX = A'

Y = X * A --> DY/DX = A

Y = A' * X * B --> DY/DX = A * B'

Y = A' * X' * B --> DY/DX = B * A'

dX'/dX = I

d(AX)'/dX = A'

dY/dX' = (dY'/dX)'

d(UV')/dX = (dU/dX)V' + U(dV'/dX)

d(U'V)/dX = (dU'/dX)V + (dV'/dX)U'

d(X'A)/dX = (dX'/dX)A + (dA/dX)X' = IA + 0X' = A

d(AX)/dX' = (d(X'A')/dX)' = (A')' = A

d(X'AX)/dX = (dX'/dX)AX + (d(AX)'/dX)X = AX + A'X