Exact hess template

[FreyJo]

No description provided.

[giaf]

@FreyJo please upload blasfeo and try again
giaf/blasfeo@2569492

[giaf]

pull blasfeo and try again :p
giaf/blasfeo@e33e163

[FreyJo]

@giaf great that worked 👌

[zanellia]

It looks good to me! On the other side I do not know much about exact Hessians in acados. I guess, especially for this PR, @giaf can give much more useful comments.

[FreyJo]

I am glad writing additional tests already paid off.
One of the ones added found a bug related to #545 , which is why
7756dc0 failed
Namely, the regularization has to be called directly before the QP solve, at least for CONVEXIFY.
@zanellia and I would have expected it to be independent of the right hand sides, which seems to be not true.
Maybe @giaf can give some insight..

Anyway, I want to merge this tomorrow, if there are no further comments.

[giaf]

The convexify regularization method aims at giving the exact solution in the case the reduced Hessian is positive definite. It is based on a recursion analogue to backward Riccati recursion, and dynamics equation enters in the computation of the cost transfer between stages.
In Robin's thesis, this is done only for the case of b=0, and consequently r and q are unchanged by the convexification algorithm. However, in the implementation I correctly address the most general case of b!=0, which results in corrections also for the terms r and q.
So, surely convexification can not happen before r and q are computed.
The current implementation does not consider currently active inequality constraints, so convexification should safely be placed also before the initial value embedding.

[FreyJo]

@giaf thanks for the insight!
However, I dont understand the last sentence:

The current implementation does not consider currently active inequality constraints [...]

Isn't this a reason for it to happen before the initial value embedding?
Because some constraint might become active due to the new initial value and therefore will not be considered then..

[...], so convexification should safely be placed also before the initial value embedding.

Just from playing around with this, I know that convexification can not be placed before the initial value embedding..