Abstract
Most software that implements interior-point methods for linear programming formulates the linear algebra at each iteration as a system of normal equations. This approach can be extremely inefficient when there are dense columns in the constraint matrix, because the density of the normal equations matrix is then much greater than the constraint matrix and the system is expensive to solve. In this report we describe an approach for improving the efficiency of this case, by special handling the dense columns using a Schur-complement approach and conjugate gradient iteration. We report some numerical results with the code PCx, into which our technique now has been incorporated.
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