[Csdp] Problems with large SDP problems

[Marcus P S]

Hello all,

  I am using SDP to perform maximum likelihood estimation of data for
some physical problems, but I am running into some strange behaviour
when the SDP problem becomes larger.

  Given an integer parameter N, the SD matrix has 2 blocks, one of
size 4^N and the other 2^(N+1), while there are 4^N+1 constraints. The
problem runs fine for randomly generated instance of size N=1,2,3,4.
However, when I run random instances for N=5, I always end up with the
dual objective function "running away" (quickly running up to >1E14),
finally giving up with the message

Stuck at edge of dual feasibility, giving up.
Failure: return code is 6
Primal objective value: -1.0208180e+14
Dual objective value: 4.1157109e+14
Relative primal infeasibility: 4.99e-01
Relative dual infeasibility: 8.87e-07
Real Relative Gap: 1.00e+00
XZ Relative Gap: 2.00e-01
DIMACS error measures: 4.99e-01 0.00e+00 6.46e-06 0.00e+00 1.00e+00 2.00e-01
Elements time: 15.671315
Factor time: 3.575801
Other time: 275.737643
Total time: 294.984759

and the resulting answer being very far from the correct solution.  I
assume that this is an issue that can be addressed by tweaking the
parameters of the numerical algorithm, but I am not sure how to do it.
I tried changing "minstepfrac" and "maxstepfrac" but if anything that
only made things worse.

If anyone has run into similar problem or has some useful pointers, I
would greatly appreciate it.

Below you can find instances of the SDP problems I have been running.

https://gist.github.com/1295649 (N=1)
https://gist.github.com/1295650 (N=2)
https://gist.github.com/1295782 (N=3)
https://gist.github.com/2957fede27de2f8d08ee (N=4)
https://gist.github.com/1296077 (N=5)

(The last file was too large for gist, so I gzipped and then uuencoded)

Best,
Marcus