Imagine I want to minimize a function F with scipy.optimize.minimize (Python). F is quite cumbersome, the jacobian J can be computed analytically but its expression is extremely nasty (lengthy). My question is: is it always best to pass J to minimize(), when it is known, or sometimes in cases such as the one at hand it is better to go with a 2- or 3-points estimation of it via F?
I guess that when J is lengthy both things happen if you pass it to minimize(): J won't be accurately evaluated and the minimization process becomes slow. Am I right?
