[Coin-ipopt] Least square system singular while initializing equality multipliers.
Nguyen An Danh
andanh at iam.rwth-aachen.de
Thu Dec 29 12:32:10 EST 2005
Hi Andreas.
When I used ISCALE = 3 or ISCALE = 4, it did not help too. With ISCALE = 4,
Ipopt run, but ||C|| became too big then decreased very slowly.
I also tried DFSCALE = 1.d-3 and ISCALE = 4 ( I reaaly do not understand
completely this parameter), but it did not become better although it ran
longer!
Here is my small example:
min -x[97]
C[i,j] x[j] =0 18 linear equalities (i=1,18; j=1,96)
F(xj)<=0.0 24 nonlinear inequalities
-infinity < x[1],...,x[96] < +infinity
0 < x[97]
slack variables <=0
The values of some F(xj) could be very near to zero. I choose x0 = 0. But my
Jacobian of constraints of linear equalities are C[i,j], which are different
from zero.
The Jacobian of linear equations are order of 0.006 to 10. And the Jacobian of
nonlinear inequalities are order of 1e-15 to 1e+3. Is it the difficulty?
Did Ipopt push out the near zero value of Jacobian?
Is it the reason that I often get the message:
Constraints not dependent.
Hessian not dependent.
when Ipopt tried to scale my problem? Are they redundant ? If I ignore them,
could I get the approximate solution as the original problem?
Since my C[i,j] has a lot of fill-in, could I remodel my problem as follows:
min -x[97]
(C[1,j] x[j])^2 + (C[2,j] x[j])^2 +... + (C[18,j] x[j])^2=0 1 nonlinear
equality (j=1,96)
F(xj)<=0.0 24 nonlinear inequalities.
By the way, could you take a look my code for the above bounds?
---------------------------------
ILB(1)=97
BNDS_L(1)=0.0d0
DO I=1,num_slackvar
IUB(I)=97+I
BNDS_U(I)=0.0D0
END DO
Thank you so much.
Danh.
On Friday 23 December 2005 20:25, you wrote:
> Hi Danh,
>
> The message "Least square system singular while initializing equality
> multipliers." means that the matrix in Equation (36) in
>
> http://www.research.ibm.com/people/a/andreasw/papers/ipopt.pdf
>
> is singular. This means that the constraint Jacobian does not have full
> row rank, or at least is numerically at the border of not having
> full row rank.
>
> This can happen if you pose constraints that are redundant (or at least
> close to being linearly dependent), and/or if your problem is still badly
> scaled. Since you using the old version of Ipopt, you could try the
> automatic scaling option ISCALE = 3 and 4 (if you have the required
> Harwell routines compiled into Ipopt), and see if that helps.
>
> Regards,
>
> Andreas
>
> On Thu, 22 Dec 2005, Nguyen An Danh wrote:
> > Dear Andreas,
> >
> > Could you tell me about the message: "Least square system singular while
> > initializing equality multipliers." ?
> >
> > I am now executing another problem (please see below). I do not know why
> > I can not excute the problem. Although the total of variables is small.
> >
> > I reread your instruction about ||C||, and try to follow your tips to
> > choose a better starting point. But I failed!!! It 's really very stuff
> > to choose suitable starting point.
> >
> > Thank you so much.
> >
> > Parameter IMAXITER has multiple assignments - using
> > 0.10000D+05 .
> > *************************************************************************
> >***** This program contains IPOPT, a program for large-scale nonlinear
> > optimization. IPOPT is released as open source under the Common Public
> > License (CPL). For more information visit www.coin-or.org/Ipopt
> > *************************************************************************
> >*****
> >
> > Going to allocate double precision work space of size 10795497
> > integer work space of size 15870830
> >
> >
> > Number of variables : 86017
> > of which are fixed : 0
> > Number of constraints : 17333
> > Number of lower bounds : 1
> > Number of upper bounds : 12288
> > Number of nonzeros in Jacobian: 1606464
> > Number of nonzeros in Hessian : 331777
> > get_scale: |g|_inf = 1.0000000000000
> > get_scale: QFSCALE = 1.0000000000000
> > get_scale: smallest CSCALE = 0.24641104282206
> >
> > ITER ERR MU ||C|| ||YPY|| ||PZ|| ||D|| ALFA(V)
> > ALFA(X) NU #LS F #cor Regu CPU(s)
> > 0 .400D+05p .100D+00 .427D+07 .000D+00 .000D+00 .000D+00 .000D+00
> > .000D +00 .000D+00 0 -.51601698D+03 0 .000D+00 .205D+03
> > Least square system singular while initializing equality multipliers.
> > Setting multipliers to zero.
> > ma27_call: LIWMA increased from 5103977 to 26726960
> > ma27_call: LA increased from 8063622 to 26726960
> > ma27_call: LIWMA increased from 26726960 to 67659177
> > ma27_call: LA increased from 26726960 to 67659177
> > ma27_call: LIWMA increased from 67659177 to 172652595
> > ma27_call: LA increased from 67659177 to 172652595
> >
> > _______________________________________________
> > Coin-ipopt mailing list
> > Coin-ipopt at list.coin-or.org
> > http://list.coin-or.org/mailman/listinfo/coin-ipopt
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