A primal deficient-basis simplex algorithm for linear programming

The standard basis, which plays a fundamental role in simplex methodology, was recently extended to include a deficient case (with fewer columns than rows) by taking advantage of primal degeneracy. Computational results have been favorable with dense implementations. In this paper, we propose a primal simplex algorithm using sparse LU factors of deficient bases. Amenable to real-world linear programming problems, which are often degenerate or even highly degenerate, the algorithm would solve them with potentially improved stability compared to the simplex algorithm.