[Csdp] Differences between versions 5 and 6
aguilera at santafe-conicet.gov.ar
Thu Feb 28 17:52:51 EST 2008
On 28 Feb 2008, at 18:30, Brian Borchers wrote:
>> In a previous message (December 2007,
>> you mentioned that using second order cone constraints as SDP
>> constraints could lead to numerical problems. Would you have
>> 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!
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