I have recently been learning how to use CVX to solve some simulation problems in communications, and I now have some difficulties in trying to write out this objective function. I would appreciate your help.

Here is the simulation problem and the symbol \Re indicates the real part of a complex number.

\underset{\mathbf{v}_{k}}{\operatorname{minimize}} \sum_{k=1}^{K} \left\{\operatorname{Tr}\left(\mathbf{V}_{k}^{H} \mathbf{A} \mathbf{V}_{k}\right)-2 \Re\left\{\operatorname{Tr}\left(\mathbf{B}_{k} \mathbf{V}_{k}\right)\right\}\right\}

Where \mathbf{V} is the variable I need to optimise, its subscript k represents the number of users and the matrices \mathbf{A} and \mathbf{B}_k are both known matrices.

I would be very grateful if I could get an answer from you.

I will assume `A`

is symmetric psd, otherwise I believe this is not convex.

The 2nd term is affine, so can be entered into CVX “as is”.

Reformulate `trace(V(:,:,k)'*A*V(:,:,k)) = square_pos(norm(sqrtm(A)*V(:,:,k),'fro'))`

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Thank you very much for your answer, the matrix \mathbf{A} is indeed a symmetric PSD. I have completed the optimization of this problem in CVX, thanks very much.