Solving large-scale linear multicommodity flow problems with an active set strategy and proximal-ACCPM

Operations Research

Volumn 54, Issue 1, 2006, Pages 184-197

  Babonneau, F ^a   Du Merle, O ^b   Vial, J P ^a  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b Air France   (France)

Author keywords

Analytic center cutting plane method, active set strategy; Network, linear multicommodity flow

Indexed keywords

APPROXIMATION THEORY; LAGRANGE MULTIPLIERS; PROBLEM SOLVING; SET THEORY;

ANALYTIC CENTER CUTTING-PLANE METHOD, ACTIVE SET STRATEGY; NETWORK, LINEAR MULTICOMMODITY FLOW;

LARGE SCALE SYSTEMS;

EID: 33644555514     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.1050.0262     Document Type: Article

References (16)

1. Castro, J. 2000. A specialized interior-point algorithm for multicommodity network flows. SIAM J. Optim. 10(3) 852-877.
2. Chardaire, P., A. Lisser. 2002. Simplex and interior point specialized algorithms for solving non-oriented multicommodity flow problems. Oper. Res. 50(2) 260-276.
3. Dantzig, G. B., P. Wolfe. 1961. The decomposition algorithm for linear programming. Econometrica 29(4) 767-778.
4. Dijkstra, E. W. 1959. A note on two problems in connection with graphs. Numer. Math. 1 269-271.
5. du Merle, O., J.-P. Vial. 2002. Proximal ACCPM, a cutting plane method for column generation and Lagrangian relaxation: Application to the p-median problem. Technical report, Logilab, University of Geneva, Geneva, Switzerland.
6. Farvolden, J. M., W. B. Powell, I. J. Lustig. 1993. A primal partitioning solution for the arc-chain formulation of a multicommodity network flow problem. Oper. Res. 41(4) 669-693.
7. Frangioni, A., G. Gallo. 1999. A bundle type dual-ascent approach to linear multicommodity min-cost flow problems. INFORMS J. Comput. 11(4) 370-393.
8. Goffin, J.-L., A. Haurie, J.-P. Vial. 1992. Decomposition and nondifferentiable optimization with the projective algorithm. Management Sci. 38(2) 284-302.
9. Goffin, J. L., J. Gondzio, R. Sarkissian, J.-P. Vial. 1996. Solving nonlinear multicommodity flow problems by the analytic center cutting plane method. Math. Programming 76 131-154.
10. Kelley, J. E. 1960. The cutting plane method for solving convex programs. J. SMM 8 703-712.
11. Larsson, T., D. Yuan. 2004. An augmented Lagrangian algorithm for large scale multicommodity routing. Comput. Optim. Appl. 27(2) 187-215.
12. Lemaréchal, C. 1977. Bundle methods in nonsmooth optimization. C. Lemaréchal, R. Mifflin, eds. IIASA Proceedings Series, Vol. 3. Pergamon Press, Oxford, UK, 79-102.
13. Mamer, J. W., R. D. McBride. 2000. A decomposition-based pricing procedure for a large-scale linear program: An application to the linear multicommodity flow problem. Management Sci. 46 693-709.
14. McBride, R. D. 1998. Progress made in solving the multicommodity flow problem. SIAM J. Optim. 8(4) 947-955.
15. McBride, R. D., J. W. Mamer. 2001. Solving the undirected multicommodity flow problem using a shortest path-based pricing algorithm. Networks 38(4) 181-188.
16. Ouorou, A., P. Mahey, J.-P. Vial. 2000. A survey of algorithms for convex multicommodity flow problems. Management Sci. 46 126-147.