[Ipopt] solving maxflow as LP

[Sebastian Nowozin]

Dear Tamas,

Adding to what others have said before: efficiency in optimization is
about making use of the problem-specific structure.
IpOpt is a great solver, but it is very general and not well suited to
solve large linear programs.  You really want a LP or network flow
solver.

For a free solver you might want to try the COIN-OR Clp solver, which
-- besides being a great LP solver -- has limited support for network
matrices.
Benchmarks for large network LPs are here:
http://plato.asu.edu/ftp/network.html

The easiest method to find an efficient solver for your problem is to
produce your problem in a standard format such as MPS and test it on
evaluation versions of Mosek and Gurobi.  Mosek in particular might be
a good candidate to test.

Good luck,
Sebastian