Fast Cholesky factorization for interior point methods of linear programming

Every iteration of an interior point method of large scale linear programming requires computing at least one orthogonal projection. In practice, Cholesky decomposition seems to be the most efficient and sufficiently stable method. We studied the ‘column oriented’ or ‘left looking’ sparse variant of the Cholesky decomposition, which is a very popular method in large scale optimization. We show some techniques such as using supernodes and loop unrolling for improving the speed of computation. We show numerical results on a wide variety of large scale, real-life linear programming problems.