Function log( log( 1 + exp(x) )) is involved in my problem which is concave. However, the concavity is not recognized by cvx. So, how to express this function in cvx?
How to express this concave function in cvx?
I doubt it is possible, I’m afraid. CVX cannot handle every function that is provably convex; it can only handle those whose convexity can be proven using its existing set of rules.
Thanks very much. I wonder whether it is possible to allow cvx in the future version to recognize the concavity of this function. 
No, due to the particular way CVX works it is almost certain never to happen. See the FAQ…