[Clp] on alternative factorizations for barrier method

[Petru Pau]

With the native factorization, CLP solves with barrier a rather big LP 
(12397 rows, 767497 columns, 6704873 elements) in more than 59 000 seconds.

CPLEX and Gurobi solve the same LP in 130 and 100 seconds, respectively.

Dense factorization does not seem to bring any improvement.

I tried all alternative factorizations mentioned in the FAQ. I was able 
to compile and link AMD and Taucs (on Windows, with Microsoft Visual 
Studio compiler). For Mumps I need a Fortran compiler, for CHOLMOD I 
could not find makefiles for win32, and WSMP is not  (and will not be) 
freely available for win32.

Anyway.

No matter what factorization I use, the iterations reported by CLP give 
the same numerical values, in lines like:

16 Primal 50944522 Dual -424542454 Complementarity 5523133 - 0 fixed, 
rank 12397

I know that the chosen factorizations is employed, I inserted messages 
at the beginning and end of order(), factorize() and solve() functions 
in ClpCholeskyTaucs.cpp and ClpCholeskyUfl.hpp, and these messages are 
displayed.

I have no knowledge about barrier method, but I am a bit perplexed: Is 
it supposed to be this way?  Is the factorization needed only for, I 
don't know, computing faster an iteration? (In any case, 18 iterations 
with Taucs took longer than 39 iterations with native factorization.) It 
seems that no matter what factorization I use, CLP follows the same 
trajectory in its search for a solution.

If the answer to the question above is rather immediate after a quick 
search in documentation, I apologize. Yet there is still a question to 
ask: Is there any chance to solve with CLP, in reasonable time, 
similarly big LPs?

Regards,
Petru