[Ipopt] bug in finite difference Jacobian

[Stefan Vigerske]

Hi,

thanks for catching this and providing a fix. I've committed this to 
trunk and it should make it to the next release.

Stefan

On 01/13/2018 02:36 PM, Enrico Bertolazzi wrote:
> I wish to signal an error in finite difference Jacobian computation.
> In line 2388 of file src/Interfaces/lpTNLPAdapter.cpp there is this piece of code:
> 
>          // Compute the finite difference Jacobian
>          for (Index ivar = 0; ivar<n_full_x_; ivar++) {
>            if (findiff_x_l_[ivar] < findiff_x_u_[ivar]) {
>              const Number xorig = full_x_pert[ivar];
>              Number this_perturbation =
>                findiff_perturbation_*Max(1., fabs(full_x_[ivar]));
>              full_x_pert[ivar] += this_perturbation;
>              if (full_x_pert[ivar] > findiff_x_u_[ivar]) {
>                full_x_pert[ivar] = xorig - this_perturbation;
>              }
>              retval = tnlp_->eval_g(n_full_x_, full_x_pert, true, n_full_g_,
>                                     full_g_pert);
>              if (!retval) break;
>              for (Index i=findiff_jac_ia_[ivar]; i<findiff_jac_ia_[ivar+1]; i++) {
>                const Index& icon = findiff_jac_ja_[i];
>                const Index& ipos = findiff_jac_postriplet_[i];
>                jac_g_[ipos] =
>                  (full_g_pert[icon]-full_g_[icon])/this_perturbation;
>              }
>              full_x_pert[ivar] = xorig;
>            }
>          }
> 
> the code (al line 2395) when the test full_x_pert[ivar] > findiff_x_u_[ivar]
> is true change the increment (computed at line 2392)
> 
> full_x_pert[ivar] += this_perturbation ; (= xorig + this_perturbation)
> 
> to (see line 2396)
> 
> full_x_pert[ivar] = xorig - this_perturbation;
> 
> but the finite difference approximation (at line 2404) is
> 
> jac_g_[ipos] = (full_g_pert[icon]-full_g_[icon])/this_perturbation;
> 
> thus the sign of the ratio is wrong.
> In practice when finite difference are computed on a point touching
> the limit the computed value has sign changed.
> 
> A simple workaround id to change line 2396
> 
>                full_x_pert[ivar] = xorig - this_perturbation;
> 
> with
> 
>                this_perturbation = -this_perturbation ; full_x_pert[ivar] = xorig + this_perturbation;
> 
> can some developer fix the error?
> 
> 
> Enrico Bertolazzi
> __________________________________________________________________________
> Dipartimento di Ingegneria Industriale
> Università degli Studi di Trento
> http://www.ing.unitn.it/~bertolaz
> 
> 
> 
> 
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