Parallel interior-point solver for structured linear programs

Mathematical Programming

Volumn 96, Issue 3, 2003, Pages 561-584

  Gondzio, Jacek ^a   Sarkissian, Robert ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

INTERIOR-POINT METHOD; LINEAR PROGRAMS; OBJECT ORIENTED LIBRARIES; OPTIMIZATION OF NETWORK; OPTIMIZATION PROBLEMS; OPTIMIZATION SOFTWARE; PARALLEL IMPLEMENTATIONS; PARALLEL SYSTEM; SEQUENTIAL IMPLEMENTATION; SPECIAL STRUCTURE;

OBJECT ORIENTED PROGRAMMING; OPTIMIZATION;

PARALLEL PROCESSING SYSTEMS;

EID: 13544254921     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-003-0379-5     Document Type: Article

References (28)

1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice-Hall, NewYork, 1993
2. Andersen, E.D., Gondzio, J., Mészáros, C., Xu, X.: Implementation of interior point methods for large scale linear programming. In: Interior Point Methods in Mathematical Programming, T. Terlaky, ed., Kluwer Academic Publishers, 1996, pp. 189-252
3. Arnold, K., Gosling, J., Holmes, D.: The Java Programming Language, Third Edition. Addison-Wesley, NewYork, 2000
4. Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numer Math, 4, 238-252 (1962)
5. Bertsekas, D.P., Tsitsiklis, J.N.: Parallel an Distributed Computations. Prentice-Hall, Englewood Cliffs, 1989
6. Birge, J.R., Qi, L.: Computing block-angular Karmarkar projections with applications to stochastic programming. Management Sci. 34, 1472-1479 (1988)
7. Björck, A.: Numerical Methods for Least Squares Problems. SIAM, Philadelphia, 1996
8. Castro, J.:A specialized interior-point algorithm for multicommodity network flows. SIAM J. Optim. 10, 852-877 (2000)
9. Choi, I.C., Goldfarb, D.: Exploiting special structure in a primal-dual path following algorithm. Math. Prog. 58, 33-52 (1993) (Pubitemid 23686632)
10. Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton, 1963
11. Dantzig, G.B.,Wolfe, P.: The decomposition algorithm for linear programming. Econometrica 29, 767-778 (1961)
12. Ferris, M.C., Horn, D.J.: Partitioning mathematical programs for parallel solution. Math. Prog. 80, 35-62 (1998)
13. Fourer, R.: Staircase matrices and systems. SIAM Rev. 26, 1-70 (1983)
14. Fragniére, E., Gondzio, J., Sarkissian, R., Vial, J.-P.: Structure exploiting tool in algebraic modeling languages. Management Sci. 46, 1145-1158 (2000)
15. Gondzio, J., Sarkissian, R.,Vial, J.-P.: Using an interior point method for the master problem in a decomposition approach. Eur. J. Operational Res. 101, 577-587 (1997) (Pubitemid 127399943)
16. Grigoriadis, M.D., Khachiyan, L.G.: An interior point method for bordered block-diagonal linear programs. SIAM J. Optim. 6, 913-932 (1996)
17. Gropp,W., Lusk, E.: User's guide to MPICH, a portable implementation of MPI.Tech. ReportANL/MCSTM- ANL-96/6, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, USA, 1996
18. Hurd, J.K., Murphy, F.M.: Exploiting special structure in a primal-dual interior point methods. ORSA J. Comput. 4, 39-44 (1992)
19. Jessup, E.R., Yang, D., Zenios, S.A.: Parallel factorization of structured matrices arising in stochastic programming. SIAM J. Optim. 4, 833-846 (1994)
20. Jones, K.L., Lustig, I.J., Farvolden, J.M., Powell, W.B.: Multicommodity network flows: the impact of formulation on decomposition. Math. Prog. 62, 95-117 (1993)
21. Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partioning graphs. The Bell System Technical Journal 29, 291-307 (1970)
22. Lustig, I.J., Marsten, R.E., Shanno, D.F.: Interior point methods for linear programming: computational state of the art. ORSA J. Comput. 6, 1-14 (1994)
23. Minoux, M.: Network synthesis and optimum network design problems: Models, solution methods and applications. Networks 19, 313-360 (1989)
24. Ridge, D., Becker, D., Merkey, P., Sterling, T.: Beowulf: Harnessing the power of parallelism in a pileof- PCs. Proceedings, IEEE Aerospace, 1997
25. Sarkissian, R.: Telecommunications Networks: Routing and survivability optimization using a central cutting plane method, PhD thesis, École Polytechnique Fédérale de Lausanne, CH-1205 Ecublens, November 1997
26. Schultz, G., Meyer, R.R.: An interior point method for block angular optimization. SIAM J. Optim. 1, 583-602 (1991)
27. Todd, M.J.: Exploiting special structure in Karmarkar's linear programming algorithm. Math. Prog. 41, 81-103 (1988)
28. Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, 1997