# [Ipopt] Very Slow convergence rate

Andreas Waechter awaechter.iems at gmail.com
Thu Mar 22 22:23:25 EDT 2012

```Hi,

If you solved the problem with Mosek, you must have provided the Hessian
matrix, correct?  If so, why don't you give the Hessian also to Ipopt?
This will certainly improve convergence, at least in terms of iteration
counts.  If you are using the L-BFGS option because your Hessian is
dense, you might want to play with the "acceptable_" termination
criteria.  Finally, I would always use the derivative checker to make
sure the derivatives are indeed correct.

Andreas

On 03/22/2012 09:05 PM, paras tiwari wrote:
> Hello,
>
> I was trying to solve a quadratic convex optimization problem in
> IPOPT. The objective function is quadratic and convex, and I was using
> limited-memory option to approximate hessian. The objective function
> value was decreased rapidly at the beginning, but it decreased
> slightly in later iterations. IPOPT did not converge, and it either
> stopped at maximum iteration or  threw "Restoration phase Failed"
> error. I solved the same problem using Mosek, and it's pretty fast and
> it converged at the global minimum. Any suggestion would be highly
> appreciated.
>
> Thank You,
> Paras
>
> Here is
>
>
> ******************************************************************************
> This program contains Ipopt, a library for large-scale nonlinear
> optimization.
>  Ipopt is released as open source code under the Common Public License
> (CPL).
> ******************************************************************************
>
>
> Number of nonzeros in equality constraint Jacobian...:        0
> Number of nonzeros in inequality constraint Jacobian.:   205361
> Number of nonzeros in Lagrangian Hessian.............:        0
>
>
> Total number of variables............................:     1092
>                      variables with only lower bounds:        0
>                 variables with lower and upper bounds:     1092
>                      variables with only upper bounds:        0
> Total number of equality constraints.................:        0
> Total number of inequality constraints...............:     1489
>         inequality constraints with only lower bounds:        0
>    inequality constraints with lower and upper bounds:        0
>         inequality constraints with only upper bounds:     1489
>
> iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du
> alpha_pr  ls
>    0  2.0230492e+03 0.00e+00 1.75e+01   0.0 0.00e+00    -  0.00e+00
> 0.00e+00   0
>    1  1.6490451e+03 4.26e-14 1.45e+01  -4.5 3.54e+00    -  1.69e-02
> 1.00e+00f  1
>    2  1.1222267e+03 5.68e-14 8.02e-01   0.5 2.09e+01    -  9.58e-01
> 1.00e+00f  1
>    3  7.7570431e+02 8.53e-14 4.20e+00  -0.0 1.20e+01    -  9.94e-01
> 1.00e+00f  1
>    4  4.1287003e+02 6.39e-14 7.19e+00  -0.8 2.54e+01    -  8.28e-01
> 8.38e-01f  1
>    5  5.3114831e+01 8.79e-14 9.83e-01  -6.4 2.09e+01    -  3.64e-01
> 8.05e-01f  1
>    6  2.5938399e+01 1.18e-13 1.90e-02  -2.8 4.56e+00    -  9.02e-01
> 9.99e-01f  1
>    7  2.5857683e+01 1.20e-13 2.78e-01  -2.8 4.18e+00    -  1.00e+00
> 3.94e-03f  1
>    8  3.9173220e+01 1.14e-13 6.04e-01  -0.1 1.41e+02    -  7.19e-03
> 1.62e-02f  1
>    9  2.7548619e+01 1.12e-13 3.09e-01  -1.9 5.36e+00    -  7.51e-01
> 3.91e-01f  1
> A few last iterations are:
> 2992  1.2285442e+01 1.05e-13 3.90e-01  -6.2 2.34e-03    -  1.00e+00
> 2.78e-01h  1
> 2993  1.2285445e+01 8.53e-14 1.43e+00  -6.2 5.62e-02    -  3.08e-01
> 1.25e-01f  4
> 2994  1.2285445e+01 9.15e-14 1.32e+01  -6.2 2.77e-01    -  1.00e+00
> 3.90e-03f  4
> 2995  1.2285442e+01 1.06e-13 2.42e-01  -6.2 3.50e-03    -  1.00e+00
> 1.00e+00h  1
> 2996  1.2285441e+01 1.07e-13 7.47e-01  -6.2 2.15e-03    -  1.00e+00
> 1.00e+00h  1
> 2997  1.2285456e+01 7.28e-14 1.75e+00  -6.2 1.01e-02    -  1.00e+00
> 1.00e+00H  1
> 2998  1.2285456e+01 1.24e-13 2.47e+00  -6.2 1.95e-02    -  1.00e+00
> 9.31e-10h 31
> 2999  1.2285450e+01 1.02e-13 1.43e+00  -6.2 1.02e-02    -  3.85e-01
> 5.00e-01f  2
> iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du
> alpha_pr  ls
> 3000  1.2285450e+01 1.32e-13 1.10e+00  -6.2 9.22e-02    -  2.68e-01
> 2.05e-03h  6
>
>
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