Interior point methods for linear programming: Computational state of the art

A survey of the significant developments in the field of interior point methods for linear programming is presented, beginning with Karmarkar's projective algorithm and concentrating on the many variants that can be derived from logarithmic barrier methods. Full implementation details of the primal-dual predictor-corrector code OB1 are given, including preprocessing, matrix orderings, and matrix factorization techniques. A computational comparison of OB1 with a state-of-the-art simplex code using eight large models is given. In addition, computational results are presented where OB1 is used to solve two very large models that have never been solved by any simplex code.