[Coin-ipopt] choosing smaller pivot tolerance to reduce fill-in

[Andreas Waechter]

Hi Frank,

I'm sending parts of my reply to your latest message to the mailing list,
since it might be of more general interest.

Running the model that you sent me, I noticed that the output says

ITER     ERR       MU      ||C||    ||D||   ALFA(X) #LS        F         Regu
    0 .374E+02p .100E+00 .104E+04 .000E+00 .000E+00   0 0.20250000E+02 .000E+00
 ma27_call:  LIWMA increased from 968930 to 11221280
 ma27_call:  LA increased from 1643625 to 11221280
 ma27_call:  LIWMA increased from 11221280 to 71314890
 ma27_call:  LA increased from 11221280 to 71314890

If you see those lines starting with `ma27_call' in the first
iteration, this can mean that there is a large amount of fill-in for
the factorization of the linear system.  Sometimes, it is possible to
reduce the fill-in by specifying a smaller pivot tolerance for the
linear solver.  This can be done with the `dpivtol' option.  The
default value is 1.e-8 (which is already quite small), but often
smaller values work, too (one shouldn't go below machine precision,
i.e. 1.e-16, though).  For your model, if I choose 1.e-14, the
algorithm still converges nicely, and it is faster.

Regards,

Andreas