Reformulate the convex constraint as an exponential cone

[ise...@gmail.com]

Dear all,

I am using MOSEK-CVXPY to my problem. Now, I am dealing with the following constraint:

where variable z is larger than 1. The right-hand size is a concave function of z. So the constraint defines a convex set. As it involves the exponential, I guess we might be able to reformulate the constraint as an exponential cone. In this case, I can use CVXPY to model and solve my problem with MOSEK. However, I am struggling with the reformulation. Can anyone help me or give me some hints on how to do it?

Thank you very much!

Stevie Lin

[Michal Adamaszek]

It may be hard.

Denoting your function by f(z) it it relatively straightforward to model the concave functions sqrt(f(z)) of log(f(z)). Maybe that is good enough for you?

Michal