Optimization problem

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Hi,

I have got this interesting optimization problem which I need to code
over Matlab. It goes like this:

I am given 5 4X4 matrices, say A,B,C,D,E. I have to find 5 unitary
matrices Q,R,S,T,U such that the absolute value of trace of
(AQ+BR+CS+DT+EU) is minimized.

Can anyone help me with this?

Thanks
Amit