[Ipopt] Ipopt Digest, Vol 118, Issue 7

[Pierre Martinon]

Hello Kayan,

Maybe you will be interested in our toolbox Bocop (www.bocop.org), it 
solves optimal control problems using ipopt and the 'full' 
discretization approach
(meaning the state variables x are also part of the discretized 
optimization problem, not only the control variables u. If I recall 
correctly this is sometimes
called 'simultaneous' approach vs 'sequential' approach).

This method does seem to give better convergence at the expense of the 
problem size.
Using Adolc/Colpack for the sparse derivatives, cpu time is spent from 
1/3 to 2/3 within ipopt (mumps), the remainder being for the user 
functions and their derivatives.
Among these, the Hessian of the Lagrangian usually takes more than 95%, 
however trying to use the built-in finite differences approximation gave 
more difficult convergence.

Well, all in all, it works pretty good, except maybe that it can be hard 
to get rid of some unwanted oscillations when the dynamics is linear in 
the control.

(For anyone who might be interested, the toolbox can use any Runge Kutta 
formula, with distinct controls for each stage.
I admit I usually settle down for basic midpoint, though.)

Best regards,
Pierre