[Csdp] Error code 8: System matrix is singular

[Brian Borchers]

On Thu, Dec 4, 2014 at 7:10 PM, Brian Borchers <borchers at nmt.edu> wrote:

> At each iteration of the primal-dual interior point method, a large,
> dense, symmetric and positive definite system of equations is solved to
> obtain the steps deltaX, deltay, and deltaZ.  When this error case occurs,
> it indicates that this system of equations is singular and can't be solved.
>
> This could be the result of a bug in CSDP or a problem with the
> formulation of your SDP.  If you would be willing to send me a copy of the
> problem on which this error occurs, I'd be happy to investigate the cause.
>
> On Thu, Dec 4, 2014 at 3:59 PM, <markisus at gmail.com> wrote:
>
>>  What does this error mean? Which matrix is the system matrix and why
>> would singularity be a problem?
>>
>> If it helps, here is my input file:
>> http://pastebin.com/ite3C1Vz
>>
>
After looking at your problem, it's clear that the difficulty is that you
have linearly dependent constraints.  Although your problem has 30
constraints, there are only 18 linearly independent constraints.  The
algorithm assumes that you have formulated your problem without linearly
dependent constraints- you'll have to remove the redundant constraints
before passing the problem to CSDP.

I'm attaching a version of your problem where I've removed the linearly
dependent constraints.  This solves quite easily:

> csdp testprob2.dat-s
This is a pure dual feasibility problem.
Iter:  0 Ap: 0.00e+00 Pobj:  9.1126984e+01 Ad: 0.00e+00 Dobj:
 0.0000000e+00
Iter:  1 Ap: 9.60e-01 Pobj:  3.6097681e+00 Ad: 9.60e-01 Dobj:
 0.0000000e+00
Iter:  2 Ap: 9.60e-01 Pobj:  1.4298925e-01 Ad: 9.60e-01 Dobj:
 0.0000000e+00
Iter:  3 Ap: 9.58e-01 Pobj:  6.0555298e-03 Ad: 9.58e-01 Dobj:
 0.0000000e+00
Iter:  4 Ap: 9.57e-01 Pobj:  2.5759669e-04 Ad: 9.58e-01 Dobj:
 0.0000000e+00
Iter:  5 Ap: 9.57e-01 Pobj:  1.0961309e-05 Ad: 9.59e-01 Dobj:
 0.0000000e+00
Iter:  6 Ap: 9.57e-01 Pobj:  4.6643796e-07 Ad: 9.97e-01 Dobj:
 0.0000000e+00
Iter:  7 Ap: 9.57e-01 Pobj:  1.9848423e-08 Ad: 9.69e-01 Dobj:
 0.0000000e+00
Iter:  8 Ap: 9.57e-01 Pobj:  8.4461375e-10 Ad: 9.60e-01 Dobj:
 0.0000000e+00
Success: SDP solved
Primal objective value: 1.0000000e-40
Dual objective value: 0.0000000e+00
Relative primal infeasibility: 1.41e-39
Relative dual infeasibility: 9.72e-10
Real Relative Gap: -1.00e-40
XZ Relative Gap: 3.48e-37
DIMACS error measures: 1.41e-39 0.00e+00 9.72e-10 0.00e+00 -1.00e-40
3.48e-37
Elements time: 0.001023
Factor time: 0.000078
Other time: 0.005480
Total time: 0.006581




-- 
Brian Borchers                          borchers at nmt.edu
Department of Mathematics      http://www.nmt.edu/~borchers/
New Mexico Tech                       Phone: (575) 322-2592
Socorro, NM 87801                   FAX: (575) 835-5366
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