Nonnegative object came to the result unbounded

You are in violation of CVX’s rules regarding log-concave functions.

You can find the rules in the CVX 3.0Beta Users Guide at http://web.cvxr.com/cvx/beta/doc/advanced.html#log-convexity . The rules stated there also apply to CVX 2,.1 even though they are not mentioned in the current 2.1 Users’ Guide. They are also discussed in the first answer by mcg in Log of sigmoid function .

“Regular” logistic regression can be done in CVX. See http://cvxr.com/cvx/examples/cvxbook/Ch07_statistical_estim/html/logistics.html for an example.