[Ipopt] [Coin-ipopt] Convergence criteria

Andreas Waechter andreasw at watson.ibm.com
Fri Feb 29 04:09:16 EST 2008

Hi Marina,

It's been a while that you wrote your message, I hope you are still
interested in an answer...

You made an interesting and good observation.

The issue is that the problems you mentioned are all "square" problems
that have no degrees of freedom, i.e., the number of equality
constraints and free variables is identical.  So, Ipopt is only trying
to solve a nonlinear system of equations, and there is no room to
optimize anything.

In that case, the mechanisms of the algorithms are somewhat different.
For the problems that you mentioned, Ipopt switches at some point to
the restoration phase, and it stays in there until the end.  The
convergence criterion in that case seems not to be 100% compatible
with the usualy requirement to have constraint violation less than the

This is of course not the way it should be, but at least Ipopt isn't
lying in the end and reports the correct infeasibility.

I created a ticket for this, see


so that I will fix it later.  I don't think this is very urgent, since
solving nonlinear systems of equations is not really what Ipopt is
made for, and one can still achieve a desired feasibility by
tightening the concergence tolerance.

Regards, and thanks again for reporting this,


> I'm using the last version of IPOPT (with default options) to solve
> the problems of the CUTEr collection.
> According to the manual, "EXIT: Optimal Solution Found indicates that
> Ipopt found a (locally) optimal point within the desired tolerances".
> Also, "the algorithm terminates successfully, if the (scaled) NLP
> error becomes smaller than this value, and if the (absolute) criteria
> according to dual_inf_tol, primal_inf_tol, and cmpl_inf_tol are
> met. (This is epsilon_tol in Eqn. (6) in implementation paper).  its
> default value is 10^{-08}".
> Since this (scaled) NLP error implies that the max norm of the
> constraints is less or equal to epsilon_tol (wich, in this case, is
> 10^{-08}), I would like to know why IPOPT declares it solved problems
> HATFLDF, EIGMAXA and EIGMINA successfully when the max norm of the
> constraints is greater than 10^{-08}.
> Thank you,
> Marina Andretta_______________________________________________

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