[Coin-ipopt] Least square system singular while initializing equality multipliers.

[Andreas Waechter]

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
>
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