Dear All
Hope you are doing well. I am new user in CVX.

When i consider N = 2, i get some value. but when declare N as variable CVX not solve it. How to solve this problem

I = 0.5;
x_f = 0.05;
h = 0.5;
% N = 2;
cvx_begin
variable x nonnegative
variable N nonnegative
minimize(((I*N*h*(x_f-x)*log(2))/((4 + x_f*h)*log(1+((x_f*h)/(4)))^2)))
cvx_end

The objective function has a product of the CVX variables N and x, which is against CVX’s rules. Moreover, it is neither convex nor concave. Therefore it can’t be reformulated for use in CVX.

I am not sure since there are so many parenthesis, but it seems that your function is linear in N. But if it is the case, either the minimum is 0 with N=0 or it is -\infty since N is non negative.

This is only if you showed your whole problem otherwise it may not work.