# [Coin-ipopt] IPOPT for QP problems

Andreas Waechter andreasw at watson.ibm.com
Wed Aug 10 14:04:59 EDT 2005

```Matt,

The first thing that one notices is that your problem is dense.  Is it
correct that the Hessian in your objective function is 100% dense (look at
the Number of nonzeros in Hessian)?  Also, on average, each constraint

Before looking into anything else, you should make sure that you are
telling the API the sparsity pattern of your problem correctly.  If your
problem is truely dense, then the usage of a sparse linear solver (which
is that Ipopt is using) is not very efficient.

Hope this helps,

Andreas

On Wed, 10 Aug 2005, Matthew Guthaus wrote:

> Hi,
>
> I'm using IPOPT to solve a simple equality constrained quadratic
> programming problem (I cannot find an adequate QP solver with API...
> Clp has one, but no API.). IPOPT works well on small problems,
> however, on medium problems I get the following error. Can anyone
> provide insight into the problem?
>
> Thanks,
>
> Matt
>
>
>
> Number of variables           :     2694
>     of which are fixed         :        0
> Number of constraints         :      597
> Number of lower bounds        :     2694
> Number of upper bounds        :     2694
> Number of nonzeros in Jacobian:   148230
> Number of nonzeros in Hessian :  3630165
>
> ITER     ERR       MU      ||C||    ||D||   ALFA(X) #LS
> F         Regu
>      0 .100E+03d .100E+00 .397E-02 .000E+00 .000E+00   0 0.92802159E
> +08 .000E+00
> Least square system singular while initializing equality multipliers.
> Setting multipliers to zero.
> Regularization parameter getting too large (a):  1.E+42
>      1 .265E+04d .100E+00 .397E-02 .000E+00 .000E+00-  0 0.92802159E
> +08 .000E+00
> Regularization parameter getting too large (a):  1.E+42
> solve_barrier: get_step_full returns IERR =  10
> mainloop: Error: solve_barrier ends with IERR =  10
>
> Number of iterations taken .............                      1
> Final value of objective function is.... 0.9280215934507787E+08
>
> Errors at final point                      (scaled)       (unscaled)
> Final maximal constraint violation is... 0.250111E-03    0.250111E-03
> Final value for dual infeasibility is... 0.264759E+04    0.968047E+06
> Final value of complementarity error is. 0.100000E+03    0.100000E+03
>
> The objective function was evaluated      1 times.
> The constraints were evaluated            1 times.
>
> EXIT: Linear system becomes too ill-conditioned
>
> CPU seconds spent in IPOPT and function evaluations =         36.3400
>
> IPOPT returned IERR = 10
>
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```