!Cannot perform the operation: {real affine} ./ {real affine}

One term of objective function:
where x and W are variables.
It has been proved to be a convex function.
I’d like to ask what function should be used here.

Essentially equivalent to

I will assume W > 0. This can be handled with exponential cone constraint.

variables W x z
{log(2)*x,W,z} == exponential(1)
z - W  % Use in place of W×exp(log(2)*x/W)-1)

In your original problem, you would use log(2)*t1*x as the first argument on the LHS.

Thank you for your reply. Can you explain it in detail from the perspective of code implementation? In addition, is there no function in CVX that can calculate b × (2 ^ (a / b) - 1)?
In essence, the formula is a deformation of b × log(1+a/b).

And, in fact, W > 0, x ≥ 0.

I provided the detailed code implementation.

y*2^(x/y) = y*exp(log(2)*x/y) , which is what I guess you already had. CVX also does not support log2(cvx_expression),, which you need to rewrite as log(cvx_expressio)/log(2).

Thank you very much for your help. I understand. I will try to modify the code.

BTW, b * log(1+a/b) can be expressed as -rel_entr(b,b+a)