[Ipopt] Very Slow Convergence
Andreas Waechter
andreasw at watson.ibm.com
Fri Feb 25 10:45:24 EST 2011
Hi Uwe,
I agree with Frank's observation; it appears that the algorithm is trying
to get out of a nonconvex region (therefore the Hessian modifications),
but it takes a lot of time. You may also want to try what happens if you
provide a different starting point (not sure how much work you put into
your starting point, given that this is probably a problem with multiple
local minima, the choice of the starting point might make a big difference
in terms of which local solution Ipopt converges to).
Regards,
Andreas
On Fri, 25 Feb 2011, Frank E. Curtis wrote:
> I agree with Ashu that the Hessian may be the issue. Not necessarily
> that it is being evaluated incorrectly, but your problem appears to be
> highly nonconvex, requiring Ipopt to modify the Hessian during all
> iterations. (Note the fourth-to-last column of the output, "lg(rg)";
> whenever this value is not "-" it means the Hessian is being
> modified.) You may want to try adjusting the way the Hessian is
> modified or use Hessian approximation techniques. You may get lucky.
>
> Frank E. Curtis
> P. C. Rossin Assistant Professor
> Industrial and Systems Engineering
> Lehigh University
> 200 W. Packer Ave., Room 322
> Bethlehem, PA 18015
> frank.e.curtis at gmail.com
> +1.646.789.5490
> http://coral.ie.lehigh.edu/~frankecurtis
>
> On Fri, Feb 25, 2011 at 10:11 AM, Ashutosh Mahajan <asm4 at lehigh.edu> wrote:
>> How do you input your problem: AMPL or your own interface? Slow convergence is
>> sometimes a sign of incorrectly evaluated hessian.
>>
>> --
>> regards
>> Ashutosh Mahajan
>> http://coral.ie.lehigh.edu/~asm4
>>
>> On Fri, Feb 25, 2011 at 01:52:51PM +0100, Uwe Nowak wrote:
>>> Hello!
>>>
>>> I am trying to solve some circle packing related problems with IPOPT.
>>> For small to medium size problems (up to 400 Circles) everything works
>>> fine and reasonable fast. However for larger problems the Algorithm does
>>> not converge..
>>>
>>>
>>>> This is Ipopt version 3.9.2, running with linear solver ma27.
>>>>
>>>> Number of nonzeros in equality constraint Jacobian...: 0
>>>> Number of nonzeros in inequality constraint Jacobian.: 1426360
>>>> Number of nonzeros in Lagrangian Hessian.............: 733017
>>>>
>>>> Total number of variables............................: 2535
>>>> variables with only lower bounds: 0
>>>> variables with lower and upper bounds: 0
>>>> variables with only upper bounds: 0
>>>> Total number of equality constraints.................: 0
>>>> Total number of inequality constraints...............: 356590
>>>> inequality constraints with only lower bounds: 356590
>>>> inequality constraints with lower and upper bounds: 0
>>>> inequality constraints with only upper bounds: 0
>>>>
>>>> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
>>>> 0 1.7720393e+06 1.99e-01 6.18e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
>>>> 1 1.7719897e+06 1.90e-03 1.97e-01 -1.0 1.99e-01 0.0 9.90e-01 9.90e-01f 1
>>>> 2 1.7719792e+06 8.17e-07 4.14e-01 -1.0 9.04e-02 -0.5 9.91e-01 1.00e+00f 1
>>>> 3 1.7719639e+06 1.63e-07 1.90e-02 -1.0 1.74e-01 -1.0 1.00e+00 1.00e+00f 1
>>>> 4 1.7719359e+06 1.46e-06 1.15e-02 -2.5 3.34e-01 -1.4 1.00e+00 1.00e+00f 1
>>>> 5 1.7718661e+06 1.31e-05 4.24e-02 -3.8 2.42e+00 -1.9 1.00e+00 1.00e+00f 1
>>>> 6 1.7718414e+06 1.85e-06 7.36e-03 -3.8 2.30e-01 -1.5 1.00e+00 1.00e+00f 1
>>>> 7 1.7717680e+06 1.66e-05 5.97e-03 -3.8 5.44e-01 -2.0 1.00e+00 1.00e+00f 1
>>>> 8 1.7717406e+06 2.34e-06 5.97e-03 -3.8 2.04e-01 -1.5 1.00e+00 1.00e+00f 1
>>>> 9 1.7716585e+06 2.10e-05 5.97e-03 -3.8 6.12e-01 -2.0 1.00e+00 1.00e+00f 1
>>>> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
>>>> 10 1.7716278e+06 2.96e-06 5.97e-03 -3.8 2.29e-01 -1.6 1.00e+00 1.00e+00f 1
>>>> 11 1.7715352e+06 2.66e-05 7.90e-03 -3.8 1.10e+00 -2.1 1.00e+00 1.00e+00f 1
>>>> 12 1.7712588e+06 2.39e-04 1.40e-02 -3.8 2.06e+00 -2.5 1.00e+00 1.00e+00f 1
>>>> 13 1.7704321e+06 2.15e-03 5.96e-03 -3.8 6.18e+00 -3.0 1.00e+00 1.00e+00f 1
>>>> 14 1.7679654e+06 1.92e-02 5.94e-03 -3.8 1.85e+01 -3.5 1.00e+00 1.00e+00f 1
>>>> 15 1.7606816e+06 1.70e-01 7.13e-03 -3.8 5.49e+01 -4.0 1.00e+00 1.00e+00f 1
>>>> 16 1.7398125e+06 1.45e+00 5.77e-02 -3.8 1.59e+02 -4.4 1.00e+00 1.00e+00f 1
>>>> 17 1.6839562e+06 2.44e-01 4.15e-01 -3.8 4.34e+02 -4.9 1.00e+00 1.00e+00F 1
>>>> 18 1.6647120e+06 1.52e+00 5.50e-02 -3.8 1.52e+02 -4.5 1.00e+00 1.00e+00f 1
>>>> 19 1.6134541e+06 2.81e-01 3.22e-01 -3.8 4.06e+02 -5.0 1.00e+00 1.00e+00F 1
>>>
>>>
>>> Then many hours later...
>>>
>>>> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
>>>> 8270 3.4629818e+05 3.73e-04 3.03e-01 -5.7 3.05e+00 -5.1 3.40e-01 1.28e-02h 1
>>>> 8271 3.4629149e+05 2.48e-04 2.48e-01 -5.7 1.14e+00 -4.7 7.40e-01 3.48e-01h 1
>>>> 8272 3.4627186e+05 3.18e-04 1.68e-01 -5.7 3.48e+00 -5.2 3.53e-01 3.38e-01h 1
>>>> 8273 3.4627111e+05 3.06e-04 1.62e-01 -5.7 1.29e+00 -4.8 3.95e-02 3.56e-02h 1
>>>> 8274 3.4626946e+05 3.00e-04 3.55e-01 -5.7 4.43e+00 -5.2 3.53e-01 2.57e-02h 1
>>>> 8275 3.4626407e+05 2.44e-04 2.17e-01 -5.7 1.45e+00 -4.8 1.64e-01 2.25e-01h 1
>>>> 8276 3.4626263e+05 2.40e-04 3.19e-01 -5.7 5.92e+00 -5.3 1.53e-01 2.01e-02h 1
>>>> 8277 3.4625715e+05 2.04e-04 1.82e-01 -5.7 1.64e+00 -4.9 4.42e-02 2.05e-01h 1
>>>> 8278 3.4624521e+05 2.74e-04 1.60e-01 -5.7 7.71e+00 -5.3 1.65e-01 1.47e-01h 1
>>>> 8279 3.4624204e+05 2.54e-04 3.19e-01 -5.7 2.29e+00 -4.9 3.28e-01 1.05e-01h 1
>>>> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
>>>> 8280 3.4621935e+05 3.81e-04 1.10e-01 -5.7 5.50e+00 -5.4 3.91e-02 2.53e-01h 1
>>>> 8281 3.4621741e+05 3.61e-04 3.22e-01 -5.7 2.06e+00 -5.0 3.66e-01 5.74e-02h 1
>>>> 8282 3.4621398e+05 3.54e-04 3.55e-01 -5.7 6.18e+00 -5.4 1.30e-01 3.39e-02h 1
>>>> 8283 3.4620558e+05 3.05e-04 2.46e-01 -5.7 2.32e+00 -5.0 1.74e-01 2.22e-01h 1
>>>> 8284 3.4620029e+05 3.03e-04 2.70e-01 -5.7 6.95e+00 -5.5 2.38e-01 4.65e-02h 1
>>>> 8285 3.4619775e+05 2.88e-04 3.07e-01 -5.7 2.61e+00 -5.1 2.54e-01 5.98e-02h 1
>>>> 8286 3.4618951e+05 2.97e-04 3.08e-01 -5.7 7.80e+00 -5.5 8.89e-02 6.48e-02h 1
>>>
>>>
>>>
>>> I read the 90-minutes-introduction to IPOPT and the implementation
>>> paper. However I do not really have a feeling, why the algorithm is
>>> converging that slow.
>>>
>>> this run is started with the options
>>> tol 0.01
>>> acceptable_tol 0.05
>>> max_iter 200000
>>>
>>> So by default it should by
>>> dual_inf_tol = 1
>>> constr_viol_tol = 1e-4
>>> compl_inf_tol = 1e-4
>>>
>>> I see, that dual feasibility is stisfied but primal feasibility is not.
>>> I do not know, where to read the compl_inf value in the current
>>> iteration. Further I do not know, if the primal and dual step sizes are
>>> "small"...
>>>
>>> Has anybody some suggestions, why the algorithm is converging that slow?
>>>
>>> Thank you,
>>> Uwe
>>>
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>>
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