# Can CVX solve the equivalent Lagrangian dual of a convex optimization problem?

My primal problem is convex, and I derived its dual form. Futher, a simplified equivalent problem of the Lagrangian dual was constructed which is formulated as follows:

maximize log det { ( diag (x) - x*x’ ) * A }
subject to
e’*x = 1
x >= 0

where x are the dual variables to be optimized, A is a known symmetric positive definite matrix and e is a column vector with all entries be one. “diag” represents the diagonal matrix with x as the diagonal elements.

I solved the model with CVX as follows:

cvx_begin
variable x(n)
maximize( det_rootn( ( diag (x) - x*x’ ) *A ) )
subject to
ones(1,n)*x == 1;
x >= 0;
cvx_end

There was an error during execution : “Disciplined convex programming error:
Only scalar quadratic forms can be specified in CVX” .

I have known the expression violated the ruleset. But I still want to confirm whether the above problem originated from a convex one can be solved with CVX if I reformulate it in the right form which is in accordance with the DCP ruleset.

Can anyone give me some suggestions? Thank you!

How did you prove that your original problem was convex? I am not certain it is, frankly. But that’s not why I am asking: I’m asking because that proof may reveal how to express the problem in CVX.