New preconditioners for KKT systems of network flow problems

SIAM Journal on Optimization

Volumn 14, Issue 3, 2004, Pages 894-913

  Frangioni, A ^a   Gentile, C ^b  

^a UNIVERSITY OF PISA   (Italy)

^b CNR   (Italy)

Author keywords

Interior point algorithms; Min cost flow problems; Preconditioned conjugated gradient method; Triangulated graphs

Indexed keywords

EID: 4043052305     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S105262340240519X     Document Type: Article

References (25)

1. R. AHUJA, T. MAGNANTI, AND J. ORLIN, Network Flows: Theory, Algorithms and Applications, Prentice Hall, Englewood Cliffs, NJ, 1993.
2. W. ANDERSON AND T. MORLEY, Eigenvalues of the Laplacian of a graph, Linear and Multilinear Algebra, 18 (1985), pp. 141-145.
3. M. BERN, J. GILBERT, B. HENDRICKSON, N. NGUYEN, AND S. TOLEDO, Support-graph precon-ditioners, SIAM J. Matrix Anal. Appl., submitted.
4. J. CASTRO, A specialized interior-point algorithm for multicommodity network flows, SIAM J. Optim., 10 (2000), pp. 852-877.
5. D. CHEN AND S. TOLEDO, Vaidya's preconditioners: Implementation and experimental study, Electron. Trans. Numer. Anal., 16 (2003), pp. 30-49.
6. D. CVETKOVIC, M. DOOB, AND H. SACHS, Spsctra of Graphs, Academic Press, New York, 1979.
7. A. FRANGIONI AND S. S. CAPIZZANO, Spectral analysis of (sequences of) graph matrices, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 339-348.
8. A. FRANGIONI AND C. GENTILE, Interior Point Methods for Network Problems, Tech. report 539, IASI-CNR, Rome, 2000.
9. K. GREMBAN, G. MILLER, AND M. ZAGHA, Performance evaluation of a parallel preconditioner, in Proceedings of the 9th IEEE International Parallel Processing Symposium, Santa Barbara, CA, 1995, pp. 65-69.
10. J. JÚDICE, J. PATRICIO, L. PORTUGAL, M. RESENDE, AND G. VEIGA, A study of preconditioners for network interior point methods, Comput. Optim. Appl., 24 (2003), pp. 5-35.
11. D. KARGER AND N. SREBRO, Learning Markov networks: Maximum bounded tree-width graphs, in Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, ACM Press, New York, SIAM, Philadelphia, 2001, pp. 392-401.
12. N. K. KARMARKAR AND K. G. RAMAKRISHNAN, private comunication, 1988.
13. S. MEHROTRA AND J. WANG, Conjugate gradient based implementation of interior point methods for network flow problems, in Linear and Nonlinear Conjugate Gradient-Related Methods, L. Adams and J. Nazareth, eds., SIAM, Philadelphia, 1996, pp. 124-142.
14. L. PORTUGAL, F. BASTOS, J. JÚDICE, J. PAIXAO, AND T. TERLAKY, An investigation of interior-point algorithms for the linear transportation problem, SIAM J. Sci. Comput., 17 (1996), pp. 1202-1223.
15. L. PORTUGAL, M. RESENDE, G. VEIGA, AND J. JÚDICE, A truncated primal-infeasible dual-feasible network interior point method, Networks, 35 (2000), pp. 91-108.
16. M. RESENDE AND P. PARDALOS, Interior point algorithms for network flow problems, in Advances in Linear and Integer Programming, J. Beasley, ed., Oxford University Press, Oxford, UK, 1996, pp. 147-187
17. M. RESENDE AND G. VEIGA, An implementation of the dual affine scaling algorithm for minumum-cost flow on bipartite uncapacited networks, SIAM J. Optim., 3 (1993), pp. 516-537.
18. M. RESENDE AND G. VEIGA, An efficient implementation of a network interior point method, in Network Flows and Matching: First DIMACS Implementation Challenge, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 12, D. Johnson and C. McGeoch, eds., AMS, Providence, RI, 1993, pp. 299-348.
19. T. ROOS, T. TERLAKY, AND J.-P. VIAL, Theory and Algorithms for Linear Optimization: An Interior Point Approach, John Wiley, Chichester, UK, 1997.
20. D. ROSE, Triangulated graphs and the elimination process, J. Math. Anal. Appl., 32 (1970), pp. 597-609.
21. R. TARJAN AND M. YANNAKAKIS, Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs, SIAM J. Comput., 13 (1984), pp. 566-579.
22. P. VAIDYA, Solving Linear Equations with Symmetric Diagonally Dominant Matrices by Constructing Good Preconditioner, Tech. report, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, 1990.
23. C. WALLACHER AND U. ZIMMERMANN, A combinatorial interior point method for network flow problems, Math. Programming, 56 (1992), pp. 321-335.
24. S. WRIGHT, Primal-Dual Interior-Point Methods, SIAM, Philadelphia, 1997.
25. M. YANNAKAKIS, Computing the minimum fill-in is NP-complete, SIAM J. Alg. Disc. Meth., 2 (1981), pp. 77-79.