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CTK Exchange
Jim
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Jul-06-06, 08:22 PM (EST) |
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"matrix algebra"
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I am trying to solve a matrix optimization problem.
Can anyone help in solving this?I need to maximize |AZB|^2+|AZC|^2 with respect to the matrix Z with the restriction that Z should be diagonal.
A-row vector 1*N
Z N*N diagonal
B-col vector N*1
C-col vector N*1
All the elements are complex numbers. |.| indicates the magnitude of the complex number. I think |AZB|^2+|AZC|^2 = |ABZ|^2+|ACZ|^2
since Z is diagonal. thanks for your time
Jim.
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sfwc
Member since Jun-19-03
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Jul-07-06, 07:34 AM (EST) |
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1. "RE: matrix algebra"
In response to message #0
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>I need to maximize |AZB|^2+|AZC|^2 with respect to the
>matrix Z with the restriction that Z should be diagonal.
Are there any other restrictions? Currently this value may be made arbitrarily large. Let X be diagonal and such that k = |AXB|^2 + |AXC|^2 is nonzero. Then if Z = nX we have |AZB|^2 + |AZC|^2 = kn^2 which can be made as big as you like.Thankyou sfwc
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Jim
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Jul-07-06, 07:13 PM (EST) |
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2. "RE: matrix algebra"
In response to message #1
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thanks for the reply. I forgot to mention a trace constraint. Here is the complete problem. I need to maximize |AZB|^2+|AZC|^2 with respect to the
matrix Z with the restriction that Z should be diagonal and trace(z)=1. Is this problem solvable?
Is it possible to obtain an optimal matrix Z* in terms of A, B and C? thanks
jim |
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