# Convex optimization problem using two sdp

A problem is described in the snapshot. I have to optimize it using the CVX tool. all the entries are given but i am having a problem because it has to be maximized over two variables Z and u. kindly some one help me how to defined multiple variable to solve this problem, Z= complex and u= double data type.
can I apply alternate optimization here, in ist step solve for Z and for u separately?

CVX allows as many variable declarations as you want, either as separate variable statements, or in some circumstances, as described at http://cvxr.com/cvx/doc/basics.html#variables in a single variables statement.

It would be a good idea for you to read or re-rad the enitire CVX Usersâ€™ Guide.

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can you help me with this, my cvx prog =m is giving +infinity

variable Z(N+1,N+1)  symmetric
variable u(X+1,X+1)  symmetric
maximize(real(trace( (Tu*Z)+u*(Vu+1) )))
subject to
real(trace((Te*Z)+u*(Ve+1)))=1;
trace(U*Z)=u;

cvx_end


The CVX output clearly states the problem is unbounded.

If you are trying to implement the model in the first post, you need to constrain Z and u to be semidefinite. The easiest way is to change symmetric to semidefinite in the variable declarations. Is u (\mu) supposed to be a scalar? Iâ€™ll let you figure that out, itâ€™s â€śyourâ€ť model, in the sense that you got it out of a paper or book. Semidefinite for a scalar just means nonnegative, as apparently the constraint on it is intended to be.

The equality constraints must use == not =. The program as written has assignments, not equality constrains. Actually, I would expect real(trace((Te*Z)+u*(Ve+1)))=1;and trace(U*Z)=u; to produce error messages. However, the image you show has ==, not = That bespeaks a lack of care in preparing your post, which does not serve the cause of minimizing the time and effort required for forum readers to help you.

If that doesnâ€™t cure the unboundedneess, then