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Thread Subject:
matrix problem

Subject: matrix problem

From: Frank

Date: 1 Aug, 2011 05:23:13

Message: 1 of 2

Hello, I have a problem about matrix.

Let a_k be a M by 1 vector and C_k be a M by M Hermitian matrix, where k = 1,2,...,K.

Define f(z) = sum_{k=1}^K (z^T a_k a_k^T z)/(z^T C_k z)

where z be a M by 1 vector.

If a_k and C_k, k =1,2,...,K, are known, how can we find z so that f(z) is minimized?

Thanks.

Subject: matrix problem

From: Bruno Luong

Date: 1 Aug, 2011 08:59:28

Message: 2 of 2

"Frank " <allinone_2003@yahoo.com.hk> wrote in message <j15d81$3ff$1@newscl02ah.mathworks.com>...
> Hello, I have a problem about matrix.
>
> Let a_k be a M by 1 vector and C_k be a M by M Hermitian matrix, where k = 1,2,...,K.
>
> Define f(z) = sum_{k=1}^K (z^T a_k a_k^T z)/(z^T C_k z)
>
> where z be a M by 1 vector.
>
> If a_k and C_k, k =1,2,...,K, are known, how can we find z so that f(z) is minimized?
>

Did you write down the corresponding Euler-lagrange's system? My guess is you'll get a complicated system and brute force minimization (e.g., FMINUNC) is the way to go.

Bruno

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