I told you x1*log(1+x2) is indefinite, which means that its Hessian with respect to x1 and x2 has both positive and negative eigenvalues, and therefore the expression is neither convex nor concave. However, I don’t think that’s what’s being done in the paper extract you just provided. it is critical that you pay attention to which symbols are optimization variables (decision variables , i.e., what would be CVX variables) vs. which are input data to the optimization problem.
In each term in the difference expression, there is a term which is of the form addressed in Writing a constraint in DCP complient format and can be implemented using rel_entr. . It is then up to you to handle the difference of convex (or concave) functions aspect to implement an algorithm in CVX.