Pi, lam and t - problem formulation


What is pi, lam and t from ocp_nlp_out related to?
I can not seem to find any variables with these names in the problem formulation: https://github.com/acados/acados/blob/master/docs/problem_formulation/problem_formulation_ocp_mex.pdf

From the getter documentation it says:

pi: multipliers for dynamics equality constraints
lam: multipliers for inequalities
t: slack variables corresponding to evaluation of all inequalities (at the solution)
sl: slack variables of soft lower inequality constraints
su: slack variables of soft upper inequality constraints

But unfortunately that didn’t make it any clearer.
Where does these variables enter the equations and what can we, as the general user, use these variables for?

Regards Thomas

Hi Thomas,

I wrote the documentation you quoted and hope to make it more clear.

I think the descriptions for pi and lam can be understood with some optimization knowledge.
Maybe I should write Lagrange multipliers instead of multipliers.

Do you have a question wrt these?

The slack variables t are less intuitive.
They are used internally, to deal with the inequality constraints.
Their initialization has very little influence on the solver.
As a general user, I would not use them.