General-purpose preconditioning for regularized interior point methods

Preconditioning Indefinite Systems in Interior Point Methods for Optimization

Every Newton step in an interior-point method for optimization requires a solution of a symmetric indefinite system of linear equations. Most of today’s codes apply direct solution methods to perform this task. The use of logarithmic barriers in interior point methods causes unavoidable ill-conditioning of linear systems and, hence, iterative methods fail to provide sufficient accuracy unless a...

Preconditioning Indefinite Systems in Interior-Point Methods for quadratic optimization

A new class of preconditioners is proposed for the iterative solution of symmetric indefinite systems arising from interior-point methods. The use of logarithmic barriers in interior point methods causes unavoidable ill-conditioning of linear systems and, hence, iterative methods fail to provide sufficient accuracy unless appropriately preconditioned. Now we introduce two types of preconditione...

Augmentation Preconditioning for Saddle Point Systems Arising from Interior Point Methods

We investigate a preconditioning technique applied to the problem of solving linear systems arising from primal-dual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased ill-conditioning of the (1, 1) block of the saddle point matrix. We demonstrate performance of the preconditioner on prob...

Interior-point methods for optimization

This article describes the current state of the art of interior-point methods (IPMs) for convex, conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and comment on the applicability of this class of methods, which have revolutionized the field over the last twenty years.

Interior-point Methods