Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM

References

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