There are a couple of formulations in Minimize log(1+1/x) where 0<x<inf . Use
z/b in place of
x, and divide everything by
log(2) to make it
log2 instead of
log. You can get the same argmax without dividing by
The problem as stated will be considered as ill-posed, because, assuming b > 0, the optimal solution is z = \infty, which the solvers CVX call will never get to.