variable A(n,n) symmetric
variable An(n,n) symmetric
variable B(n,n) symmetric
variable b(n)
maximize( det_rootn( An ) )
subject to
norms( A * x + b * ones( 1, m ), 2 ) <= 1;
B == diag( sqrt ( diag (A) ) )^-1;
An == B * A * B;
Minimum (or maximum) volume ellipsoid problems are very finicky. You simply can’t do everything you want in a convex setting. Some formulations support maximization, some support minimization. I’m going to bet that yours is not convex, and therefore CVX cannot solve it. But you should check chapter 8 of Boyd & Vandenberghe to be sure.