[Ipopt] Slack too small, adjusting variable bound

[Andreas Waechter]

Hi Per-Ola,

The message means that the method computing scaling factors for the linear 
system (you must be using MC19) are either very large or NaN/Inf.  This 
can also be caused by very small slacks, and an ill-conditioned problem. 
Since the algorithm is making progress, it is probably not that bad, but 
you could swtich the scaling off.  You could also see if something in your 
problem is not scaled well 
(https://projects.coin-or.org/Ipopt/wiki/HintsAndTricks#Scalingoftheoptimizationproblem).

Andreas

On Sun, 20 Feb 2011, Per-Ola Larsson wrote:

> Thanks for you explaination Hans!
>
> Another error I get from IPOPT is "Scaling factors are invalid - setting
> them all to 1."
>
> Here is a printout from IPOPT,
> Scaling factors are invalid - setting them all to 1.
>  103  9.0234276e+00 7.32e-02 2.97e+03  -1.9 8.83e-01    -  4.25e-01
> 1.00e+00h  1
> Scaling factors are invalid - setting them all to 1.
>  104  9.0087841e+00 6.69e-03 1.05e+01  -1.9 2.57e-01    -  1.00e+00
> 1.00e+00h  1
> Scaling factors are invalid - setting them all to 1.
>  105  8.1631880e+00 2.04e-01 2.11e+01  -2.3 1.39e+00    -  1.00e+00
>
> The steps look OK except the error message. Anyone knows that what might
> be wrong?
>
> Best regards,
> Per-Ola
>
> Hans Pirnay wrote:
>> The slacks z should converge to z_i*x_i  = \mu. The warning you are
>> seeing appears when a slack z becomes smaller than \eps*\mu, where
>> \eps is machine precision. Therefore, bad scaling where some of your
>> primal variables become way too large, might be an issue. Another case
>> where this problem comes up is when your problem fails to satisfy the
>> constraint qualifications (LICQ or at least MFQC) and the second order
>> sufficient condition - as soon as some variables or multipliers are
>> not uniquely defined, weird behavior appears.
>>
>> So the first thing to check for is scaling of variables and
>> constraints such that the gradients are similar in scale, and then for
>> redundant constraints.
>>
>> best
>>
>> hans
>>
>> On Fri, Feb 18, 2011 at 9:30 AM, Per-Ola Larsson <perola at control.lth.se> wrote:
>>> Hello!
>>>
>>> When solving my optimization problem in IPOPT I often get messages of
>>> the kind
>>>
>>> In iteration X, 1 Slack too small, adjusting variable bound.
>>>
>>> What is the origin of this error? Is my problem badly scaled? What can I
>>> do to not get this error?
>>>
>>> Best regards,
>>> --
>>> Per-Ola Larsson, MScEE, PhD Student
>>>
>>> Dept. of Automatic Control     E-mail: per-ola.larsson at control.lth.se
>>> Lund University                WWW:    www.control.lth.se/~perola
>>> Box 118                        Phone:  +46 (0)46 - 222 87 93
>>> S-221 00 Lund, Sweden          Fax:    +46 (0)46 - 13 81 18
>>>
>>>
>>>
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>
>
>
>
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