[Csdp] Differences between versions 5 and 6

[Nestor Aguilera]

On 28 Feb 2008, at 18:30, Brian Borchers wrote:

>> In a previous message (December 2007,
>> <http://list.coin-or.org/pipermail/csdp/2007-December/000005.html>),
>> you mentioned that using second order cone constraints as SDP
>> constraints could lead to numerical problems. Would you have 
>> references
>> for that?
>
> A simple transformation from SOCP to SDP is discussed in the book by
> Nesterov and Nemirovski.  I think it's also in Boyd and Vandenberghe.

I am using the transformation(s) indicated in notes by Nemirovski 
(2002, downloaded from internet).

> Because the transformation takes an n element vector in an SOCP
> constraint and turns it into an n by n matrix block in an SDP, it's
> definitely going to use a lot of memory and will probably slow things
> down substantially.  Furthermore, when I actually tried this on some
> problems from the DIMACS Challenge, I found that the resulting SDP's
> were very hard for CSDP and the other available SDP codes to solve-
> the primal dual interior point method often just failed to converge.
> I'm not aware of any published papers that discuss this though.

Is that completely (or almost) solved by using a sparse Cholesky 
factorization? Will CSDP have it in the future?

As always, thanks!

Nestor