When solve with ipopt, we can use Jax to calculate the hessian matrix and jacobian instead of providing it ourselves. However, ipopt with Jax is very slow for large problems.
If we calculate the hessian matrix and jacobian ourselves and use the Problem interface, we can define their structures. Defining the hessian matrix and jacobian structures will make the solver faster, especially if sparse.
Can we use the Jax library to calculate the hessian matrix and jacobian and still be able to define the structures? I want to take the power of both.
Otherwise, using the problem interface and not Jax will be better.
Problem interface: https://cyipopt.readthedocs.io/en/stable/tutorial.html