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;

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.