# [Coin-ipopt] IPOPT for QP problems

Matthew Guthaus mguthaus at eecs.umich.edu
Wed Aug 10 15:33:17 EDT 2005

```I double checked this and my Hessian is definitely not 100% dense. I
use my own functions to implement the objective function and its
derivatives. The 2nd derivative returns an element of a matrix from
my quadratic objective. It has only a 597x597 dense submatrix out of
a 2694x2694 total size. Since it is symmetric, it has 178503 non-zero
entries out of 3630165 (~5% dense).

Is IPOPT doing something to the hessian to make things non-zero?

Matt

On Aug 10, 2005, at 2:04 PM, Andreas Waechter wrote:

> 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
> gradient has 10% non-zero elements.
>
> 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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>>
>>
>
>

```