Interior Point Methods
Nowadays, much attention is focused on primal-dual Interior Point Methods (IPMs) due to their great computational performance. IPMs have permanently changed the landscape of mathematical programming theory and computation. Most primal-dual IPMs are based on Mehrotra’s Predictor-Corrector (MPC) method. In this chapter, a presentation of the basic concepts of primal-dual IPMs is performed. Next, we present the MPC method. The various steps of the algorithm are presented. Numerical examples are also presented in order for the reader to understand better the algorithm. Furthermore, an implementation of the algorithm in MATLAB is presented. Finally, a computational study over benchmark LPs and randomly generated sparse LPs is performed in order to compare the efficiency of the proposed implementation with MATLAB’s IPM solver.
- 3.Frisch, K. F. (1955). The logarithmic potential method of convex programming. Technical report, University Institute of Economics, Oslo, Norway.Google Scholar
- 15.Von Neumann, J. (1947). On a maximization problem. Technical report, Institute for Advanced Study, Princeton, NJ, USA.Google Scholar