An implementation of preprocessing for interior point methods for linear programming

We classified preprocessing methods into (1) analytic methods, (2) methods for removing implied free variables, (3) methods using pivot or elementary row operations, (4) methods for removing linearly dependent rows and columns and (5) methods for dense columns. We noted some considerations to which should be paid attention when preprocessing methods are applied to interior point methods for linear programming. We proposed an efficient order of preprocessing methods and data structures. We also noted the recovery process for dual solutions. We implemented the proposed preprocessing methods, and tested it with 28 large scale problems of NETLIB. We compared the results of it with those of preprocessing routines of HOPDM, BPDPM and CPLEX.