A robust and efficient proposal for solving linear systems arising in interior-point methods for linear programming

The computational burden of primal-dual interior point methods for linear programming relies on the computation of the search direction by solving one or more linear systems per iterations. The objective of this work is to study an efficient and robust way of solving these systems for large-scale sparse problems. Our proposal combines the use of the stable system and a hybrid iterative method where a conjugate gradient method is preconditioned during the initial interior point iterations by an incomplete Cholesky factorization type.