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

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elgen

Posts: 7
Registered: 8/27/10
Re: Least-square optimization with a complex residual function
Posted: Oct 28, 2010 10:20 PM
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On 10-10-28 09:38 PM, kym@kymhorsell.com wrote:
> elgen<sket16@no.spam.hotmail.com> wrote:
>> I have a question on the least-square 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.

> [...]
>> 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

>
> So your resid is real now? OK. Change your mind, that's alright. :)
>

>> 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.

>
> Ahhh. At worst you can treat the resid as 2 SoS -- the real parts of r and
> the imag parts of r.
>
> For more general resid functions maybe think in terms of Euclid form.
>
>


I understand that you refer residual to

conj(r) r

in my case.

How would I proceed to calculate its gradient? Would you mind being more
specific? What is "SoS"?


elgen




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