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Topic:
Leastsquare optimization with a complex residual function
Replies:
4
Last Post:
Oct 30, 2010 11:16 AM



elgen
Posts:
7
Registered:
8/27/10


Leastsquare optimization with a complex residual function
Posted:
Oct 28, 2010 9:10 PM


I have a question on the leastsquare optimization with a complex residual function. The residual function is r(z_1, z_2), in which z_1 and z_2 are complex variables.
The LS cost function is
\sum_i r(z_1, z_2^2
where i is the number of samples.
Many textbooks discusses this problem in the context of a real residual function and  \cdot  denotes the euclidean norm.
In my case r(z_1, z_2) is a complex function. If I use the Euclidean norm (conjugated inner product), the cost function becomes
\sum_i conj(r)r
I am stuck on how to calculate the gradient of this cost function as conj(r) is not an analytic function and the gradient needs to take the derivative with respect to z_1 and z_2.
Any feedback is welcome. Thank you.
elgen



