I am using JuMP with Ipopt and encounter this problem. For example, I have a constraint looks like x^2 + y^2 <= 1. Originally I just add this constraints to the model. But when I try to define a function f(x, y) = x^2 + y^2, register this function and its gradient to the model (I tried both autodiffer and user-defined gradient), and then run the code, Ipopt actually takes more time and iterations to converge. I am wondering is this possible, or I am not coding in the correct way?
In addition, just to make sure, currently we cannot give hessian of multivariate functions, right?
Thanks in advanced.