Add in methods to scale the problem objective, constraints and their derivatives for IPOPT

[moorepants]

IPOPT converges better if the objective and constraints are scaled. We can probably make smart scaling based on the dynamics that are being modeled.

[moorepants]

If the user sets bounds on the trajectories, those could be used to make some scaling rules because the max/min of each state would be known.

[Peter230655]

If the user sets bounds on the trajectories, those could be used to make some scaling rules because the max/min of each state would be known.

Just curiosity: would scaling mean, that the values $\in (-1.0, 1.0)$ ?

[moorepants]

Yes.

[moorepants]

There is some general rule for keeping objective and constraint values small, but here is the basic documentation: https://coin-or.github.io/Ipopt/OPTIONS.html#OPT_NLP_Scaling and it ties to applying scaling to the internal linear solve routine.

[moorepants]

Tips on scaling: coin-or/Ipopt#498 (comment)