An Interior Point Method for Large Scale Linear Feasibility Problems

In engineering design processes, there are many cases where feasibility has to be checked. Some applications, such as radiation therapy, can be formulated as linear feasibility problems. In addition, a feasible point is required to start many other algorithms. In this paper, we propose an interior point method for linear feasibility problems. This algorithm is suitable for problems that are large and sparse. Convergence of the algorithm is proved. Numerical experiment results on a standard set of linear programming problems are reported. This set includes some large, hard, and highly degenerated cases. The numerical experiment shows that our proposed algorithm is efficient and robust.