An optimization problem involving matrices/tensors
- From: kasimir.blomstedt@xxxxxxxxxxx
- Date: 30 Mar 2007 13:09:26 -0700
Hi,
sorry if this is a repeat of a partial message, I had some problems
with Google. Since I've been banging my head over the problem below, I
would appreciate it if somebody had some fresh ideas or even solutions
concerning it. The problem is to find such a complex vector x and such
a complex orthogonal projection P that the functional
f(x, P) = \sum_{n = 1}^N (x' R_n x)Tr(P S_n)
is maximized. Here x' is the Hermitian conjugate of x, Tr denotes the
trace, and the matrices R_n and S_n are square and Hermitian. The
dimensions of the matrices R_n need not be the same as the dimension
of the matrices S_n, and neither dimensions need have anything to do
with N > 1.
Any ideas appreciated!,
regards,
-Kasimir Blomstedt
.
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