[Coin-ipopt] Precision Init of Vars in Equality Constraints is Key!?

[Andreas Waechter]

Hi Frank,

Sorry for not replying earlier, I just re-discovered your message in my
INBOX...

The user provided starting point makes quite difference in the behavor of
Ipopt (and any other nonlinear optimizer). However, I don't quite see how
a difference in the last digit can make such a difference in behavior (or
did you also change other parts of the model, like the dimension?).  It
would be nice if you could send me the AMPL model files for the two cases
(please not to the mailing list to avoid spamming the other subscriber's
inboxes :).  I'll try to look at some point...

Thanks for letting me know,

Andreas

On Thu, 24 Mar 2005, Frank J. Iannarilli wrote:

> Hi All,
>
>
> I've noticed that if I submit problems to IPOPT with imprecisely set
> initialization values, for variables appearing in equality constraints,
> that IPOPT can run very much longer, and perhaps more poorly!
>
> Of course, all constraints get slacks to convert to equality constraints,
> but I'm referring to user-defined equality constraints.  For example:
>
>   s.t. Sum{j=1..N} w[j] = 1
>
>   N=9, e.g., initialize w[j] = 1/N = 1/9 ~ 0.1111...
>
> 1/9 cannot be exactly represented in floating point, so the constraint is
> not initially satisfied.
>
> ====================
> For a given problem I'm playing with, I tried running per above, then
> initializing w[j] with exactly representable floating point values such
> that they summed precisely to 1.  The differences in execution:
>
>
> Precise:
> 75 iterations, 390sec CPU
>
> -----
>
> Inprecise:
> 135 iterations, 560sec CPU,
> at iteration 48: filter: Setting LAMBDA to zero after restoration phase
> after final iteration 135:
>  Restoration started with CNRM =   1.96217842E-09
>  filter: Error: resto_filter returns IERR =  18
>  solve_barrier: filter returns IERR =  18
>  mainloop: Error: solve_barrier ends with IERR =  18
>
> and non-negligible dual infeasibility.
> ==================
>
>
> Is this to be expected, and do I have the proper casual "explanation"?
>
>
> Regards,
>
>
>
> Frank J. Iannarilli, franki at aerodyne.com
> Aerodyne Research, Inc., 45 Manning Rd., Billerica, MA 01821 USA
> www.aerodyne.com/cosr/cosr.html
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