Staircase matrices and primal–dual interior point methods

Given a general linear programming model, the set of rows of the matrix A is partitioned in two subsets, B1 and B2, which allows an interior point primal dual algorithm to deal with matrices of lower order. The normal equation associated with these methods takes the form B1D²B^t1x = b. Matrix B2 is used in the calculation of D². The ultimate purpose of the paper is the application of this result to a particular class of staircase matrices.