I have a nonlinear constraint of the form: z * exp(-x) >= d where z and x are non-negative bounded variables and the lower bound of z is 0; d is a fixed positive number.
I used the logarithmic transformation to get:
ln(z)- x >= ln(d)
which would be convex if z >0. However, z can take value 0. Is there a trick to avoid this issue, taking the logarithm of a variable that can be equal to 0?
Under which condition is the function z * exp(x) concave?