[Csdp] Error code 8: System matrix is singular

[markisus at gmail.com]

Thank you for your help!





From: Brian Borchers
Sent: ‎Thursday‎, ‎December‎ ‎4‎, ‎2014 ‎9‎:‎39‎ ‎PM
To: Mark Liu
Cc: csdp at list.coin-or.org









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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