[Csdp] Couldn't get feasible solution for a moderately large SDP problem

[Brian Borchers]

When I ran your test case through SeDuMi (with pars.errors=1 to get the
DIMACS error measures), I got:

 47 :   2.24E+03 9.80E-12 0.000 0.3687 0.9000 0.9000   0.93  6  6  2.7E-06
 48 :   2.24E+03 6.68E-12 0.000 0.6815 0.9000 0.9000   0.98 11 10  1.9E-06
Run into numerical problems.

iter seconds digits       c*x               b*y
 48      2.3   6.5  2.2390568439e+03  2.2390575678e+03
|Ax-b| =   3.1e-04, [Ay-c]_+ =   1.7E-09, |x|=  1.8e+04, |y|=  4.3e+04

Detailed timing (sec)
   Pre          IPM          Post
3.022E-02    2.354E+00    3.420E-03
Max-norms: ||b||=1.800647e+01, ||c|| = 1,
Cholesky |add|=4, |skip| = 0, ||L.L|| = 516.211.

DIMACS error measures
  PInf     PConInf     DInf    DConInf    RelGap    RelComp
3.92E-08  0.00E+00  0.00E+00  2.83E-12  -1.62E-07  1.06E-04

SeDuMi wasn't able to get the relative complentarity gap below 1.0e-4, so
it clearly had difficulty with this problem.

Looking at your data file, it appears that the coefficients were rounded to
single precision before being written out.  This is a bad idea in this case
since the problem is badly conditioned.

In your testing with SeDuMi, did you start with your problem in MATLAB,
write it out in sparse SDPA format, and then read it back in before solving
the problem, or did you solve it directly with SeDuMi without going through
the data file?



On Sun, Jan 26, 2014 at 7:35 PM, Feng Nan <fnan at bu.edu> wrote:

> Hi CSDP users/developers,
> I am trying to solve a SDP problem inside a code in C. The structure of
> the SDP formulation I have is such that I can always guarantee a feasible
> solution no matter how big sample size is. CSDP successfully solves the
> problem with small sample sizes; but when the sample size grows it keeps
> giving up saying lack of progress or stuck on the edge of primal
> feasibility.
>
> I generated such a moderately large problem in SDPA sparse format
> (attached here, it has 661 constraints, 2 blocks in the X,Z matrices with
> sizes 12 -671) and fed it into MATLAB solvers such as SDPT3 and Sedumi and
> both of them gave the correct solution. Using the same input file I just
> couldn't get even a feasible solution from CSDP.
>
> I've also played with the parameters to no avail...
> Do you have any suggestions? Is there a setting to make it behave the same
> as those MATLAB solvers?
> Thank you very much!
> Feng
>
>
>
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>


-- 
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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