Regularized Symmetric Inde nite Systems in Interior Point Methods for Linear and Quadratic Optimization

This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraints. New regularization techniques for Newton systems applicable to both symmetric positive de nite and symmetric inde nite systems are described. They transform the latter to quaside nite systems known to be strongly factorizable to a form of Cholesky-like factorization. Two di erent regularization techniques, primal and dual, are very well suited to the (infeasible) primal-dual interior point algorithm. This particular algorithm, with an extension of multiple centrality correctors, is implemented in our solver HOPDM. Computational results are given to illustrate the potential advantages of the approach when applied to the solution of very large linear and convex quadratic programs.