Preconditioning indefinite systems in interior point methods for optimization

In the present paper, the authors consider the linear system arising from a subproblem in the interior-point method. Such a system is typically ill-conditioned due to the use of a barrier parameter and that the matrix involved is indefinite. This is a crucial issue in the development of optimization solvers based on interior-point methods. To solve such an ill-conditioned system efficiently, the authors propose the use of preconditioners based on the Hessian of the objective function. It is shown that the new system is well-conditioned. Promising numerical results are reported.