Dynamic range ratio minimization with cvx


I was wondering if there is a way ( I mean a “Disciplined Convex” way) to minimize or fix the dynamic range ratio of the solution vector.

For example:

    variable x(n)
    minimize( norm(A*x-b) )
    subject to
        max(x)/min(x)< alpha %this is not disciplined convex programming

Thanks in advance,

If min(x) is positive, you can do this:

max(x) <= min(x) * alpha

thanks mcg,
no, unfortunately it is not positive. It can have positive and negative values. And if I try to do :

max(abs(x)) <= min(abs(x)) * alpha 

I get the error message that it is not disciplined convex.

Any other ideas?

Thanks again

Unfortunately not, because the problem is not convex in your case. CVX cannot solve it.