# [Ipopt] irregular iteration counts of small scale problem

Stefan Vigerske stefan at math.hu-berlin.de
Thu Jun 30 06:35:22 EDT 2016

```Hi,

I could reproduce this, also with a GAMS model (attached).
Some lines from the Ipopt log short before it terminates:

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du
alpha_pr  ls
15600  9.9176715e-02 6.51e-10 8.50e-04 -11.0 7.64e-06   2.0 1.00e+00
1.00e+00h  1
15601  9.9176679e-02 5.85e-09 8.50e-04 -11.0 2.29e-05   1.6 1.00e+00
1.00e+00h  1
15602  9.9176666e-02 8.23e-10 8.50e-04 -11.0 8.59e-06   2.0 1.00e+00
1.00e+00h  1
15603  9.9176625e-02 7.41e-09 8.50e-04 -11.0 2.58e-05   1.5 1.00e+00
1.00e+00h  1

It seems to me that the steps are too small to make sufficient progress
in reducing dual infeasibility.
I played with a number of parameters, but didn't make it any better.
Reducing optimality tolerance (constr_viol_tol 1e-8, tol 0.01) was the
only thing that made Ipopt terminate fast (13 iterations).

Btw, CONOPT, MINOS, and SNOPT solve this in <10 iterations, but Knitro
also needs >10000 iterations. Seems to be a difficult problem for
interior point algorithms.

Stefan

On 06/29/2016 11:14 AM, dongming jin wrote:
> dear all:
> I'm solving a nonlinear problem which has 3 constraints and 12 variables with ipopt. But the iteration count  gets larger than 1000 and ipopt can't find an optimal solution. Can anyone help me out?
>
>
> the problem is showed below:
> objective function:
> pow(10, 6)*(x[6] + x[7] + x[8] + x[9] + x[10] + x[11])
> constraints:
>  (-x[2] * cos(x[0])) / (0.075556*x[4]) + pow(x[2], 2) / 0.075556 + x[6] - x[7]=0
>  (-x[3] * cos(x[1])) / (0.075556*x[5]) + pow(x[3], 2) / 0.075556 + x[8] - x[9]=0
>  0.1<-x[2] * cos(x[0]) / (0.075556*x[4]) - x[3] * cos(x[1]) / (0.075556*x[5]) + 1 / 0.075556*(1 / pow(x[4], 2) + 1 / pow(x[5], 2)) + x[10] - x[11]<0.3099
> variables:
> -pi/2<x[0],x[1]<pi/2;  0.95<x[2],x[3]<1.05;  0.9<x[4],x[5]<1.1;  0<x[6]~x[11]<10^7
>
>
> I guess it has something to do with the symmetrical constraints. When i set the lower bound of the third constraints to zero, ipopt found the optimal solution in the 15th iteration.and I  paste the main program in the appendix for reference.
> I would appreciate it if anyone can give me some advice.
>
>
> dongming jin
>
>
>
>
>
>
> _______________________________________________
> Ipopt mailing list
> Ipopt at list.coin-or.org
> http://list.coin-or.org/mailman/listinfo/ipopt
>

--
http://www.gams.com/~stefan
-------------- next part --------------
A non-text attachment was scrubbed...
Name: jin.gms
Type: application/unknown
Size: 864 bytes
Desc: not available
URL: <http://list.coin-or.org/pipermail/ipopt/attachments/20160630/6fbb9823/attachment.bin>
```