Parallelization of an interior point algorithm for linear programming

Abstract

In this study, we present the parallelization of Mehrotra’s predictor-corrector interior point algorithm, which is a Karmarkar-type optimization method for linear programming. Computation types needed by the algorithm are identified and parallel algorithms for each type are presented. The repeated solution of large symmetric sets of linear equations, which constitutes the major computational effort in Karmarkar-type algorithms, is studied in detail. Several forward and backward solution algorithms are tested, and buffered backward solution algorithm is developed. Heurustic bin-packing algorithms are used to schedule sparse matrix-vector product and factorization operations. Algorithms having the best performance results are used to implement a system to solve linear programs in parallel on multicomputers. Design considerations and implementation details of the system are discussed, and performance results are presented from a number of real problems.