I am trying to compare different solvers/routines on minimizing the objective function of simulated method of moments. This objective function is non-differentiable. I wonder if there is a setting in Ipopt to do numerical derivatives?
The method of differentiation in Ipopt is automatic differentiation. My understanding is that it does not apply to non-differentiable functions. So should I code the numerical Jacobian and Hessian by myself using the package FiniteDiff.jl, then register these functions as described in JuMP documents?
In general, my question is similar to this post.