I am wondering if there are ways to bound the condition number of a matrix that is being optimized?

For instance, for a simple 2 by 2 matrix A that I am trying to maximize the product of eigenvalues subject to a maximum ratio of the two eigenvalues given by tau. In practice there are other constraint LMIs in this particular problem, but I think this captures the basic issue, namely that the condition # is quasi-convex.

```
minimize(det_inv(A))
subject to
A==semidefinite(2);
lambda_max(A)>=tau*lambda_min(A);
```

yields an error: Invalid constraint: {convex} >= {concave}

even when tau =1 and the second constraint is always

satisfied by the solution even if that equation is commented out (e.g. the largest eigenvalue is >= the second eigenvalue).

Is there a smart way to recast this problem such that the constraint equation that limits the value of the condition number is convex?