[Clp] ordering methods for Clp barrier

[Kish Shen]

Hi,

I am trying to figure out what the "native" cholesky ordering that can 
be specified for the barrier method in Clp(for CbcSolver/cbc executable, 
but I assume also for clp executable). Up till now, I have been using 
ClpCholeskyDense if I am using Cbc/Clp compiled without UFL AMD support, 
and ClpCholeskyUfl if compiled with UFL AMD.

Looking at ClpCholeskyBase.cpp, it looks like ClpCholeskyBase does 
provide its own code for ordering, so is this what is used for "native" 
ordering?

I did some comparison using ClpCholeskyBase and ClpCholeskyUfl for the 
ordering of ClpInterior, and it seems ClpCholeskyBase has similar 
performance to ClpCholeskyUfl in most cases, but does seem to be better 
in more cases, and in the example I tried, has only 1 case of numeric 
difficulties (for solving my version of miplib's gen4) compared to 2 
cases for Ulf.

Looking at the comment at the start of ClpCholeskyBase.cpp, 
ClpCholeskyBase implements a Approximate Minimum Local Fill ordering, 
whereas UFL AMD, used by ClpCholeskyUfl, implements AMD, Approximate 
Minimum Degree ordering. Am I correct that these are not the same 
ordering algorithm? I have noticed that CPLEX's barrier solver provides 
approximate minimum degree and approximate minimum fill (along with 
nested dissection) as alternative orderings -- do these correspond to 
ordering provided by ClpCholeskyUfl and ClpCholeskyBase, respectively?

Cheers,

Kish

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