[Ipopt] sensitivities of ipopt's solutions

[Martin Neuenhofen]

Dear all,

I want to compute sensitivities of my Ipopt's solution's (i.e.
x) performance ( i.e. f(x) ) with respect to a real scalar perturbation p,
where d acts on the problem by modifying cL or cR by being cL:=cL + p * v,
where v is a constant vector (or analogously for cR), where cL and cR are
the left and right box borders of the non-linear constraints.

The math is simple:
Solving F(x,p)=0 for p=0 after x is the way how Ipopt solves for x, where F
is (in an ideal world) the KKT-conditions. Now, having the performance
function f, one computes the substantial derivative df/dp =
delta_f/delta_p - delta_f/delta_x * (DF/Dx)^{-1} * DF/Dp . df/dp is the
quantity of interest.

However, the following questions occur:

1) Since Ipopt does actually not solve F but only approximately an
approximation of F, I want to know if I could as well take any other
eps-KKT conditions instead of F and yield good results. Does someone have
experience in that?

2) The F of Ipopt is quite involved due to all the substitutions made from
the original problem formulation to the one where x>=0 and c=0. I thought
of always changing both cL and cR by p*v since then it should be simply
c+p*v=0. Has yet someone tried computing sensitivities from solutions of
Ipopt?

Kind regards,
Martin
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