How can I deal with this constraint in MATLAB CVX?

[Mark_L_Stone]

The first formulation violates CVX’s rules.

The second formulation complies with CVX’s log-convexity rules, which unfortunately are not documented in the CVX Users’ Guide, but are documented in

Log of sigmoid function

It might be a bit surprising to CVX power users that log(1/(1+exp(-z))) is accepted by CVX. After all, it does not seem to obey the disciplined convex programming ruleset! But in fact, in order to support geometric programming, CVX has a lesser known set of rules governing log convexity as well. The definition of log convexity is this: if a function is positive and its logarithm is convex, then it is log-convex. There are equivalent definitions of log-affine and log-concave functions as well. W…