[Ipopt] the particular L-BFGS update; feasibility enforcements; custom linear system solver in Matlab function; disable locking check

[Martin Neuenhofen]

Dear all,

we would like to use Ipopt in the following settings:

   1. How is the Hesse update of the Lagrangian computed in particular? The
   Hesse is HL, then it is HL= sigma * f + sum_i{ lambda_i * Hc_i } . Are the
   updates performed for each summand Hc_I and Hf separately or for their sum
   w.r.t. the difference from one iteration to the next. I am wondering
   because in the first case there would be no assurance of conservation of
   positive definiteness and in the second case there would be issues with
   regards to that the lambdas change. So do they then freeze the lambdas once
   for the update?
   2. For our particular application I can easily find feasible starting
   points. However, if I pass a slightly infeasible initial guess to Ipopt
   then the inf_pr simply does not converge to 10^-6 . It starts from 0.5,
   goes to 0.1, and then both the feasibility and the cost-function value grow
   with each further iteration above 10^5. I already ensured that inf_pr has
   "original" scaling. I have no idea why Ipopt fails on this one and why in
   that way (I mean I had at least expected that it would terminate and say "I
   am unable to find you a feasible point" instead of just messing everything
   up).
   3. How can I make a custom solver? I want something like an iterfunc. I
   use Matlab so I want to write my own preconditioned iterative saddle solver
   in Matlab and apply it during each iteration on the KKT system and shift it
   on my own.
   4. Can one disable the intrinsic check of Ipopt whether the system is
   overdetermined (in terms of more equality constraints than degrees of
   freedom). I want to solve such problems since the equations arise from
   discretizations so they and their solution have to be interpreted only in a
   rough manner of being satisfied. In general, does Ipopt hold any features
   for these kinds of systems (e.g. adaptive stopping criteria s.t. I do not
   run back into a point of local intersection of two (nearly) collinear
   equality constraints).

We are happy for any information on either of these bullets, please as
exhaustive as possible.

Kind regards,
Martin
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