# [Ipopt] Very Slow convergence rate

paras tiwari pbtiwari at wustl.edu
Thu Mar 22 22:05:27 EDT 2012

```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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