Optimization with respect to matrix
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Hi,
I have the following problem to solve: argmin_X || Xu - b ||^2 where u and b are given (vectors), and || . || is l-2 norm. So it looks like ordinary least squares but with optimization that goes over matrix X. Is it possible to do this in Matlab?
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Chaowei Chen
am 3 Sep. 2011
what is the dimension of u and b? But generally I think you will get infinite many solutions giving you || X*u - b || ^2 =0.
For example, say u and b are both 2D vectors. X is therefore 2 by 2 matrix, having 4 degree of freedom to let you assign values. You can arbitrarily choose x_11 and x_12 such that u_1*x_11+u_2*x_12=b_1 and u_1*x_21+u_2*x_22=b_2. Therefore, the 2-norm is zero.
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Daniel Shub
am 30 Aug. 2011
The l^2-norm does not care about the shape of your data so you can just reshape your matrix into a vector.
u = u(:);
b = b(:);
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