[Ipopt] Very Slow Convergence

Ashutosh Mahajan asm4 at lehigh.edu
Fri Feb 25 10:11:58 EST 2011


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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