Criss-cross algorithm based on the most-obtuse-angle rule and deficient basis

To improve computational efficiency, a new criss-cross algorithm based on the most-obtuse-angle pivoting index rule and deficient basis algorithm is proposed in this paper to solve linear programming problems. We do numerical test values with the 25 standard NETLIB problems, preliminary computational tests demonstrate that the new algorithm overcomes computational difficulties yielding from degeneracy, and reduces the number of iterations and the overall computation time. In addition, the new algorithm has greatly simplified unbound or infeasible conditions to make it more practical. So far, the numerical experimental results show that the new algorithm is promising and is able to implement under the sparse structure, in order to apply to large scale sparse problem.