Interior point methods are considered the most powerful tools for solving
linear, quadratic and nonlinear programming. In each iteration of interior
point method (IPM) at least one linear system has to be solved. The main
computational effort of I
PMs consist in the computational of these linear
systems. That drives many researchers to tackle this subject, which make this
area of research very active. The issue of finding a preconditioner for this
linear system was investigated in many papers.
In this paper, we provide a preconditioner for interior point methods for
quadratic programming. This preconditioner makes the system easier to be
solved comparing with the direct approach.
The preconditioner used follows the ideas, which is used for linear
approach. An explicit null space representation of linear constraints is
constructed by using a non-singular basis matrix identified from an estimate of
the optimal partition. This is achieved by means of efficient basis matrix
factorisation techniques used in implementations of the revised simplex
method.
