Prim-based support-graph preconditioners for min-cost flow problems

Computational Optimization and Applications

Volumn 36, Issue 2-3, 2007, Pages 271-287

  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; Prim algorithm

Indexed keywords

ALGORITHMS; CONJUGATE GRADIENT METHOD; COST BENEFIT ANALYSIS; ITERATIVE METHODS; PROBLEM SOLVING;

INTERIOR POINT ALGORITHMS; MIN-COST FLOW PROBLEMS; PRECONDITIONED CONJUGATED GRADIENT METHOD; PRIM ALGORITHMS;

TREES (MATHEMATICS);

EID: 34248197966     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-006-9005-9     Document Type: Article

References (19)

1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B. : Network Flows: Theory, Algorithms and Applications. Prentice Hall, New Jersey (1993)
2. Borghetti, A., Frangioni, A., Lacalandra, F., Nucci, C.A.: Lagrangian heuristics based on disaggregated bundle methods for hydrothermal unit commitment. IEEE Trans. Power Syst. 18, 313-323 (2003)
3. Castro, J.: A specialized interior-point algorithm for multicommodity network flows. SIAM J. Optim. 10, 852-877 (2000)
4. Crainic, T.G., Frangioni, A., Gendron, B.: Bundle-based relaxation methods for multicommodity capacitated fixed charge network design problems. Discret. Appl. Math. 112, 73-99 (2001)
5. Frangioni, A., Gallo, G.: A bundle type dual-ascent approach to linear multicommodity min-cost flow problems. INFORMS J. Comput. 11(4), 370-393 (1999)
6. Frangioni, A., Gentile, C.: Interior point methods for network problems. Technical Report 539, IASI, CNR, Roma (2000)
7. Frangioni, A., Gentile, C.: New preconditioned for KKT systems of network flow problems. SIAM J. Optim. 14(3), 894-913 (2004)
8. Frangioni, A., Manca, A.: A computational study of cost reoptimization for min-cost flow problems. INFORMS J. Comput. 18(1) 61-70 (2006)
9. Frangioni, A., Serra Capizzano, S.: Spectral analysis of (sequences of) graph matrices. SIAM J. Matrix Anal. Appl. 23(2), 339-348 (2001)
10. Jùdice, J.J., Patricio, J., Portugal, L.F., Resende, M.G.C., Veiga, G.: A study of preconditioners for network interior point methods. Comput. Optim. Appl. 24, 5-35 (2003)
11. Natazon, A., Shamir, R., Sharan, R.: Complexity classification of some edge modification problems. Discret. Appl. Math. 113, 109-128 (2001)
12. Ng, E., Peyton, B.W.: Block sparse Cholesky algorithms on advanced uniprocessor computers. SIAM J. Sci. Comput. 14, 1034-1056 (1993)
13. Pardalos, P.M., Resende, M.G.C. (eds.): Handbook of Applied Optimization. Oxford University Press, Oxford (2002)
14. Portugal, L.F., Resende, M.G.C., Veiga, G., Jùdice, J.J.: A truncated primal-infeasible dual-feasible network interior point method. Networks 35, 91-108 (2000)
15. Resende, M.G.C., Pardalos, P.M.: Interior point algorithms for network flow problems. In: Beasley, J.E. (ed.) Advances in Linear and Integer Programming, pp. 147-187. Oxford University Press, Oxford (1996)
16. Resende, M.G.C., Tsuchiya, T., Veiga, G.: Identifying the optimal face of a network linear program with a globally convergent interior-point method. In: Hager, W.W., Hearn, D.W., Pardalos, P.M. (eds.) Large-Scale Optimization: State of the Art, pp. 362-387. Kluwer Academic, Dordrecht (1994)
17. Resende, M.G.C., Veiga, G.: An implementation of the dual affine scaling algorithm for minimum cost flow on bipartite uncapacited networks. SIAM J. Optim. 3(3), 516-537 (1993)
18. Rose, D.J.: Triangulated graphs and the elimination process. J. Math. Anal. Appl. 32, 597-609 (1970)
19. Tarjan, R.E., Yannakakis, M.: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput. 13(3), 567-579 (1984)