How can I deal with this constraint in MATLAB CVX?

Uncategorized
Oct 12, 2024
M

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.

M

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?

M

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

M
Replying to #3

Thanks so much for your reply.