[Csdp] Scaling the problem to mitigate the solver "giving up"

[Jedediah Fry]

Hi CSDP users,

I'm using CSDP to solve large semidefinite programs and have run into some
difficulties with the solver.  Typically, the solver either "gives up" with
a solution that satisfies my LMIs and has an objective with a somewhat
large duality gap (-1e-01 relative real gap), or "gives up" with a solution
that does not satisfy my LMIs.   In the latter case, I believe there exists
a feasible solution, but the solver gives up with a solution outside the
feasible set. In both cases, it typically reports "Stuck at edge of dual
feasibility."

People have talked about similar issues in the CSDP archives, and Dr.
Borchers states that scaling is often a good fix (
https://list.coin-or.org/pipermail/csdp/2014-January/000125.html). I'm
unfamiliar with this approach, is there a good reference that describes
different ways to scale A and c, and how to unscale the solution obtained
from solving the scaled problem?

Also, what is the criterion that determines the solver should "give up?"
Can I change any solver parameters to prolong the effort (the routine
always "gives up" before my specified maximum iterations, and I'd the
solver to see if it can chug on the problem a little bit longer).

For reference, I've attached a problem and CSDP cannot solve but I believe
is solvable.

Thanks,
Micah Fry
 ​
 fry_prob.dat-s
<https://drive.google.com/a/vt.edu/file/d/0B-bHmaZTGpTrX1QtOVFfZ2hsd1U/view?usp=drive_web>
​
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.coin-or.org/pipermail/csdp/attachments/20170914/fadaed31/attachment.html>