Solving linear systems in interior-point methods (Q5959078)

There are two approaches to solve the linear systems in interior-point methods: the normal equation approach and the augmented system approach. The authors integrate the two methods by applying matrix partitioning to the augmented system approach. Specifically, it is shown that the Schur complement method which is applied to problems whiteness columns is a special case of the augmented system approach. This property is used for the integrates approach. If the integrated approach is used, linear systems can be solved maintaining sparsity of matrices without respect of the existence of dense columns.