Abstract
This paper addresses the role of centrality in the implementation of
interior point methods. Theoretical arguments are provided to justify
the use of a symmetric neighbourhood. These are translated into computational
practice leading to a new insight into the role of re-centering in the
implementation of interior point methods. Arguments are provided
to show that second-order correctors, such as Mehrotra's
predictor--corrector, can occasionally fail. A remedy to such
difficulties is derived from a new interpretation of multiple centrality
correctors. Extensive numerical experience is provided to show that
the proposed centrality correcting scheme leads to noteworthy savings
over second-order predictor--corrector technique and previous
implementation of multiple centrality correctors.
Key words: Linear Programming, Quadratic Programming, Interior Point Methods, Centrality Correctors.