[Ipopt] Sharpening tolerances

Paul Smith phhs80 at gmail.com
Sat Jan 29 13:53:15 EST 2011

Thanks, Andreas. I have reduced the tolerance and I am now obtaining
zero. Apparently, I am being lucky, as no numerical issue has shown up
up -- Ipopt reports:

Ipopt 3.9.2: Optimal Solution Found.

When Ipopt reports that, can one be sure that there was no numerical
issue? That is, can one be sure that the solution is not wrong because
of numerical issues?

Have a nice weekend,


On Fri, Jan 28, 2011 at 9:39 PM, Andreas Waechter
<andreasw at watson.ibm.com> wrote:
> Hi Paul,
> Ipopt generates a sequence of iterates that *converges* to the solution, but
> it might not end up exactly at the theoretical solution, only close by.  In
> your case, 1e-9 seems very close to zero (you can try to reduce the
> tolerance "tol" to less than its default 1e-8, but you might run into
> numerical issues then, due to the finite precision of he floating point
> numbers).
> In addition, Ipopt is an interior point method, and this means that will
> never generate iterates where the variables are exactly at their bounds
> (which they often are at the solution).  (Note the "bound_relax_factor" and
> "honor_original_bounds" in this context.)
> Regards,
> Andreas
> On Thu, 27 Jan 2011, Paul Smith wrote:
>> Dear All,
>> I am using Ipopt with AMPL. It works fine, but in a specific problem,
>> I get an optimal value for the objective function of
>> 1.35038e-09
>> when the solution, theoretically, is zero.
>> Is there some way of instruct Ipopt to search further to get a value
>> closer to zero?
>> Thanks in advance,
>> Paul
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