[Csdp] Differences between versions 5 and 6

[Brian Borchers]

>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.

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.