[Ipopt] Very Slow Convergence

Hans Pirnay hanspirnay at googlemail.com
Fri Feb 25 10:51:37 EST 2011 

Some more ideas:

- scaling is probably the single most important thing to look into. make
sure that - if possible - all gradients and hessian values are in a common
range of say 0.01 ... 100
- Are any of your constraints linearly dependent (or may become linearly
dependent at the solution)?

On Fri, Feb 25, 2011 at 4:23 PM, Uwe Nowak <uwe.nowak at itwm.fraunhofer.de>wrote:

> Hello!
>
> It is my own implementation (C++ interface).
>
> The derivative checker did not complain (for smaller instances) and
> several unit tests (for toy examples) worked successfully. However of
> course there might be some hidden bugs I did not find.
>
> Best Regards,
> Uwe
>
>
> Am 25.02.2011 16:11, schrieb Ashutosh Mahajan:
> > 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
> >>
> >> _______________________________________________
> >> Ipopt mailing list
> >> Ipopt at list.coin-or.org
> >> http://list.coin-or.org/mailman/listinfo/ipopt
>
>
> --
> Uwe Nowak
> Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
> Abteilung Optimierung
> Fraunhofer-Platz 1
> D-67663 Kaiserslautern
> Telefon:  +49(0)631/31600-4458
> E-Mail:   uwe.nowak at itwm.fraunhofer.de
> Internet: www.itwm.fraunhofer.de
>
> _______________________________________________
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> Ipopt at list.coin-or.org
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>
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