{log-affine} - {log-affine} is nor allowed by CVX. Read the FAQ Why isn’t CVX accepting my model? READ THIS FIRST! and the CVX Users’ Guide http://cvxr.com/cvx/doc/dcp.html .and also the answer by mxg at Log of sigmoid function .
If you show us your problem, maybe we can determine whether there is a reformulation which CVX will accept. But you should read the material I linked, and try to determine whether you have a convex problem, hopefully which can be formulated consistent with CVX’s DCP rules.