Gigaflops in linear programming

This paper describes the parallelization of an ''industrial strength'' linear programming package. Our parallel version of CPLEX Barrier, running on a Silicon Graphics Power Challenge shared-memory multiprocessor, provides dramatic performance improvements over sequential methods on a wide range of practical, realistic linear programming problems. The resulting software/hardware combination can provide sustained performance of as much as 2.4 Gflops.

[1]  I. Lustig,et al.  Computational experience with a primal-dual interior point method for linear programming , 1991 .

[2]  Robert E. Bixby,et al.  Implementing the Simplex Method: The Initial Basis , 1992, INFORMS J. Comput..

[3]  Mauricio G. C. Resende,et al.  An Implementation of the Dual Affine Scaling Algorithm for Minimum-Cost Flow on Bipartite Uncapacitated Networks , 1993, SIAM J. Optim..

[4]  Roger Grimes,et al.  The influence of relaxed supernode partitions on the multifrontal method , 1989, TOMS.

[5]  L. D. J. C. Loyens,et al.  A parallel interior point algorithm for linear programming on a network of transputers , 1993, Ann. Oper. Res..

[6]  Irvin Lustig,et al.  Feasibility issues in a primal-dual interior-point method for linear programming , 1990, Math. Program..

[7]  Sanjay Mehrotra,et al.  On the Implementation of a Primal-Dual Interior Point Method , 1992, SIAM J. Optim..

[8]  Roy E. Marsten,et al.  Feature Article - Interior Point Methods for Linear Programming: Computational State of the Art , 1994, INFORMS J. Comput..

[9]  Vipin Kumar,et al.  A parallel formulation of interior point algorithms , 1994, Proceedings of Supercomputing '94.

[10]  Edward Rothberg,et al.  Alternatives for Solving Sparse Triangular Systems on Distributed-Memory Multiprocessors , 1995, Parallel Comput..

[11]  Guangye Li,et al.  An implementation of a parallel primal-dual interior point method for block-structured linear programs , 1992, Comput. Optim. Appl..

[12]  Mauricio G. C. Resende,et al.  An implementation of Karmarkar's algorithm for linear programming , 1989, Math. Program..

[13]  Anthony Vannelli A Parallel Implementation of an Interior Point Method for Linear Programming , 1991, PPSC.

[14]  Gautam Mitra,et al.  The interior point method for LP on parallel computers , 1992 .

[15]  Irvin Lustig,et al.  An analysis of an available set of linear programming test problems , 1989, Comput. Oper. Res..

[16]  Roy E. Marsten,et al.  On Implementing Mehrotra's Predictor-Corrector Interior-Point Method for Linear Programming , 1992, SIAM J. Optim..

[17]  Patrick R. Amestoy,et al.  An Approximate Minimum Degree Ordering Algorithm , 1996, SIAM J. Matrix Anal. Appl..