L. Schork and J. Gondzio
Abstract
The implementation of a linear programming interior point solver
is described that is based on iterative linear algebra. The linear
systems are preconditioned by a basis matrix, which is updated
from one interior point iteration to the next to bound the entries
in a certain tableau matrix. The update scheme is based on simplex-type
pivot operations and is implemented using linear algebra techniques
from the revised simplex method. An initial basis is constructed
by a “crash” procedure after a few interior point iterations.
The basis at the end of the interior point solve provides
the starting basis for a crossover method, which recovers a basic
solution to the linear program. Results of a computational study
on a diverse set of medium to large-scale problems are discussed.
Key words: Interior Point Methods, Linear Programming, Basis Preconditioning.