[Ipopt] Sharpening tolerances

[Andreas Waechter]

Hi Paul,

> 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?

The message means that Ipopt found a point that satisfies the termination 
criteria for the tolerance you provided.  For the definition of the 
criteria please refer to the Ipopt implementation paper.

Regards,

Andreas


>
> Have a nice weekend,
>
> Paul
>
>
> 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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>>>
>>>
>>
>
>
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