[Csdp] A mystery

[Brian Borchers]

I agree with Imre's response- this problem has multiple optimal solutions
(all with optimal value 2/3), and CSDP happens to be returning one of those
solutions, although it isn't the solution that Ron would prefer.  
Let me just add the following.
 
Ron wrote:

>while for the phony solution we have
>Tr[F[0].Y]=1/2
...
>and for the true solution
>Tr[F[0].Y]=2/3

The F[0] from the data file is 
 
F[0]=               (pardon the fixed font here!)
 
-1 1 0
 1 0 0
 0 0 0
       0 0 0 0
       0 0 0 0
       0 0 0 0
       0 0 0 0

Ron's Y (The one that Ron thinks is optimal)  is
 
Y=

1/2           7/12       sqrt(23)/12
7/12           1               0
sqrt(23)/12    0               1
                                       7/2    0    0    0
                                        0     0    0    0
                                        0     0    0    0
                                        0     0    0   7/2

CSDP's Y is 
 
Y=

1/2           7/12             0 
7/12           1               0
0              0               1
                                       7/2    0    0    0
                                        0     0    0    0
                                        0     0    0    0
                                        0     0    0   7/2

In both cases, when I compute it by hand, I get that Tr[F[0].Y]=2/3, not 1/2!  
 
When I run my copy of CSDP on this problem, I get the solution listed above
as "CSDP's Y", and the optimal value reported by CSDP is 2/3.

It isn't clear whether Ron's CSDPGMP came up with the incorrect value of
Tr[F[0].Y]=1/2 or whether this was a mistake that was made outside of CSDP.
In the former case, that would imply a bug in CSDPGMP.