Can CVX handle a ODE as constraint?

I’m quite confident that the answer is no but I thought it was worth a shot.

I’m trying to do a joint state and parameter estimation for a friction model (very similar to the LuGre friction model).

I have a limited to no experience with CVX. I used a couple of times but, for my simple problems, the run time was higher than what it would take my code to run, so I used the CVX only as a mean to check my results (I was doing at the time an on-line parameter identification).

My questions arises from the fact that, while going through an article I’ve came across a reference ACADO Toolkit (not trying to advertise it or anything like that) that solves this type o problems - joint state and parameter estimation. They use, in the tutorial on this topic, the Gauss Newton method to solve a least-squares problem with ODE constrains. If my understanding is correct, the Gauss Newton method (which is a gradient type of method if I’m not wrong) if applicable to convex problems.

Hopefully I made myself understood.

The only linear operations that CVX understands are dense and sparse matrices. For instance, convolutions and FFTs must be represented by their matrix multiplication equivalents to use them in CVX. The same will be true for ODEs as well.

Thank you very much for your answer.