[Ipopt] Towards comprehension of IPOPT convergence behaviours
mneuen
mneuen at cs.ubc.ca
Thu Nov 22 03:23:09 EST 2018
Hi All,
For a couple of practical problems, I ran into the following phenomena,
that however I cannot reproduce in small-dimensional problems. I seek
small-dimensional comprehensible problems for each for the following
phenomena, respectively:
(a) The iteration count of IPOPT for a problem can change dramatically
when the objective function is rescaled by a factor of only 10; and it
can also affect the local minimum that IPOPT runs into.
(b) Initialized from a feasible starting point x0, IPOPT computes
infeasible iterates that eventually become so infeasible that it does
not find back to a feasible solution, and then it gives in. (Typical
error messages are: Restoration failed - or - Restoration found feasible
point that is unacceptable to the filter.)
(c) For mu=10^-4, the solution solves the eps-KKT equations. Update of
mu=10^-5 then causes very small step-sizes caused by the
globalization/step-acceptance procedure, although three iterations of
full Newton would result in interior primal-dual points (x>0,y,z>0) with
a KKT residual in norm <10^-10 for all subsequent values of mu.
I used standard options only, and always start with high-accuracy
feasible (but clearly non-optimal) initial guess x0. My problems do not
contain poles, and are well-scaled.
I am thankful to any educational examples or further explanations.
Cheers,
Martin
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