  Interior Point Methods (IPM) rely on the Newton method for solving systems of
nonlinear equations. Solving the linear systems which arise from this approach
is the most computationally expensive task of an interior point iteration. If,
due to problem's inner structure, there are special techniques for efficiently
solving linear systems, IPMs enjoy fast convergence and are able to solve large
scale optimization problems. It is tempting to try to replace the Newton method
by quasi-Newton methods. Quasi-Newton approaches to IPMs either are built to
approximate the Lagrangian function for nonlinear programming problems or
provide an inexpensive preconditioner. In this work we study the impact of
using quasi-Newton methods applied directly to the nonlinear system of
equations for general quadratic programming problems. The cost of each
iteration can be compared to the cost of computing correctors in a usual
interior point iteration. Numerical experiments show that the new approach is
able to reduce the overall number of matrix factorizations and is suitable for
a matrix-free implementation.
