[Ipopt] gradient scaling and stopping criteria

[Drosos Kourounis]

Dear Andreas,
I noticed that you are using the unscaled values
for the stopping criteria (tol excluded), although 
I have specified specified automatic gradient-based
scaling. One would expect that when the problem is 
scaled, then the stopping criteria would correspond
to the scaled values for infeasibility, complementarity etc...

Why this doesn't happen, and how could I enforce it?
It would be nice if we had a flag so that the scaled
values were considered for these thresholds if the user
has specified gradient scaling or something similar. 
If the problem is not scaled, then it makes sense to
consider the unscaled values. Could you please shed 
some light here?

Moreover, if I specify hessian approximation to be exact,
it is not clear what happens? I would expect, that if I 
do not provide any hessian information and yet I desire
exact hessian approximation, then the algorithm would 
use finite differences to calculate the columns of the 
hessian. Could you please explain how could I have IPOPT
using finite differences to approximate the Hessian 
whenever it needs it?

Best,
Drosos.