A new technique for the Simplex basis LU factorization update

The objective of this work is to develop more efficient alternatives for Simplex method implementation. Techniques of the Simplex basis LU factorization update are developed to improve the solution of the Simplex method linear systems to achieve a column static reordering of the matrix. A simulation of the Simplex method is implemented, with the change of basis obtained from MINOS. Only the factored columns actually modified by the change of the basis are carried through to achieve an efficient LU factorization update. The matrix columns are reordered according to three strategies: minimum degree, block triangular form and the Björck strategy. Sparse factorizations are obtained for any basis with only a small computational effort to obtain the order of columns, since the reordering of the matrix is static and basis columns follow this ordering. Computational results for Netlib problems show the robustness of this approach and good computational performance, since there is no need for the periodical factorizations used in traditional updating methods. The proposed method achieves a reduction in the nonzero entries of the basis with respect to MINOS.