How can I deal with this constraint in MATLAB CVX?

[Momo]

Can someone help me with
c/y^2*e^{-ax+b} \leq z in CVX, where x,y,z are variables, and a,b,c\geq0?

I’ve checked the hessian matrix of the LHS, which is positive semidefinite.

But I encountered the Disciplined convex programming error: Cannot perform the operation: {convex} .* {log-affine} when I implement it in CVX.

[Momo]

I think I found a way to manage it by expressing it as ce^{-ax+b-2log(y)}, which is acceptable by CVX.
Is this a good approach?
Btw, can someone kindly explain why the original form is not accepted while the second one is?

[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…

[Momo]

Thanks so much for your reply.