[Ipopt] Why ipopt needs so many iterations when starting from the optimal solution?

[Andreas Waechter]

Hi Pierre,

Since Ipopt is an interior point method, it needs to make sure that the 
initial point is not too close to the boundary.  For this, it perturbs the 
user-given starting point, based on the value of the options bound_frac 
and bound_push (see documentation).  Setting those to smaller values will 
lead to a smaller perturbation, and the code might converge quicker from a 
starting point close to the solution.  However, if the perturbation is too 
small, the algorithm will cut off the search direction quite a bit in the 
first iterations, leading to slow convergence.

In addition, if the starting point is very close to the solution, you 
might also want to choose a smaller value for the initial barrier 
parameter (mu_init).

Regards,

Andreas

On Wed, 9 Mar 2011, Pierre Schaus wrote:

> Hello
>
> I'm making some benchmarking between ipopt and conopt (from ampl) and
> strangely when I call solve two consecutive times (the second solve
> starting from the optimal solution) ipopt needs 235 iterations to
> rediscover this best solution while conopt only 4.
>
> Do you have an idea how to avoid all these iterations when ipopt
> starts on the optimal solution or very closely?
>
> Thank you in advance,
>
> Pierre
>
> A fragment of the output when solving again:
>
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
>
> 0 -1.6889364e+03 7.06e+01 1.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
>
> 1 -1.8076240e+03 7.06e+01 1.06e+02 -1.0 1.12e+05 - 1.12e-01 1.06e-03f 1
>
> 2 -1.7868621e+03 5.70e+01 5.00e+01 -1.0 6.42e+02 - 1.13e-01 1.92e-01h 1
>
> 3 -1.7773846e+03 5.15e+01 1.43e+02 -1.0 6.05e+02 - 2.62e-01 9.75e-02h 1
>
> 4 -1.7346472e+03 2.86e+01 2.94e+01 -1.0 6.40e+02 - 3.57e-01 4.44e-01h 1
>
> 5 -1.7138111e+03 1.80e+01 2.96e+01 -1.0 6.71e+02 - 4.02e-01 3.72e-01h 1
>
> 6 -1.6979992e+03 1.06e+01 9.60e+01 -1.0 7.65e+02 - 7.76e-01 4.09e-01h 1
>
> 7 -1.6771948e+03 2.75e+00 6.48e+01 -1.0 1.31e+03 - 2.00e-01 7.42e-01h 1
>
> 8 -1.6672749e+03 4.10e-01 1.06e+02 -1.0 9.65e+02 - 7.23e-01 9.72e-01h 1
>
> 9 -1.6663897e+03 3.55e-01 7.49e+03 -1.0 1.85e+03 - 4.22e-01 1.49e-01f 1
>
> ...
>
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
>
> 230 -1.6889365e+03 4.00e-09 1.38e-07 -8.6 6.52e-01 -9.6 1.00e+00 1.00e+00H 1
>
> 231 -1.6889365e+03 4.00e-09 5.57e+01 -8.6 3.22e+00 - 1.00e+00 1.56e-02h 7
>
> 232 -1.6889365e+03 4.00e-09 5.65e+01 -8.6 4.01e+00 - 1.00e+00 1.19e-07h 24
>
> 233 -1.6889365e+03 4.00e-09 2.07e-07 -8.6 3.11e+00 - 1.00e+00 1.00e+00H 1
>
> 234 -1.6889365e+03 4.00e-09 5.63e+01 -8.6 5.33e+00 - 1.00e+00 3.91e-03h 9
>
> 235 -1.6889365e+03 4.00e-09 5.33e-08 -8.6 9.49e-01 - 1.00e+00 1.00e+00s 22
>
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