Solving linear systems in interior-point methods

There are two approaches to solve the linear systems in interior-point methods: the normal equation approach and the augmented system approach. We integrated the two methods by applying matrix partitioning to the augmented system approach. Specifically, we show the Schur complement method which is applied to problems with dense columns is a special case of the augmented system approach. We will use this property for the integrated approach. If we use the integrated approach, we can solve linear systems maintaining sparsity of matrices without respect of the existence of dense columns.