Implementing an LU Factorization for the Embedded Network Simplex Algorithm

References

• Ahuja R., Magnanti T., Orlin J.Network Flows (1993) (Prentice Hall, Englewood Cliffs, NJ) Google Scholar
• Barnhart C. Dual ascent methods for large-scale multicommodity flow problems. Naval Res. Logist. (1993) 40:305–324Crossref, Google Scholar
• Barr R., Farhangian K., Kennington J. Networks with side-constraints: An LU factorization update. Annals Soc. Logistics Engineers (1986) 1:66–87Google Scholar
• Bixby R. Solving real-world linear programs: A decade and more of progress. Oper. Res. (2002) 50:3–15Link, Google Scholar
• Brown G., McBride R. Solving generalized networks. Management Sci. (1984) 30:1497–1523Link, Google Scholar
• Castro J. PPRN 1.0 user’s guide. (1994) . DR 94/06, Department of Statistics and Operations Research, Universidad Politécnica de Catalunya, Barcelona, SpainGoogle Scholar
• Castro J., Nabona N. Primal-dual interior point method for multicommodity network flow with side-constraints and comparison with alternative methods. (1994) . Department of Statistics and Operations Research, Universidad Politécnica de Catalunya, Barcelona, SpainGoogle Scholar
• Castro J., Nabona N. An implementation of linear and nonlinear multicommodity network flows. Eur. J. Oper. Res. (1996) 92:37–53Crossref, Google Scholar
• Frangioni A. Dual-ascent methods and multicommodity flow problems. (1997) . Ph.D. thesis, TD 5/97, Università di Pisa-Genova-Udine, Pisa, ItalyGoogle Scholar
• Grigoriadis M., Khachiyan L. An exponential-function reduction method for block-angular convex programs. Networks (1995) 26:59–68Crossref, Google Scholar
• Hellerman E., Rarick D. Reinversion with the presassigned pivot procedure. Math. Programming (1971) 1:195–216Crossref, Google Scholar
• Kennington J. A primal partitioning code for solving multicommodity network flow problems. (1979) . Technical report 79008, Department of Operations Research, Southern Methodist University, Dallas, TXGoogle Scholar
• Lustig I., Rothberg E. Gigaflops in linear programming. Oper. Res. Lett. (1996) 18:157–165Crossref, Google Scholar
• Mamer J., McBride R. A decomposition based pricing procedure for large scale linear programs: An application to the linear multicommodity flow problem. Management Sci. (2000) 46:693–709Link, Google Scholar
• Marsten R., Subramanian R., Lustig I., Shanno D. Interior point methods for linear programming: Just call Newton, Lagrange, and Fiacco and McCormick! Interfaces (1990) 20:105–116Link, Google Scholar
• McBride R. Factorization in large-scale linear programming. (1973) . Ph.D. dissertation, Anderson Graduate School of Management, University of California, Los Angeles, Los Angeles, CAGoogle Scholar
• McBride R. A spike collective dynamic factorization algorithm for the simplex method. Management Sci. (1978) 24:1031–1042Link, Google Scholar
• McBride R. A bump triangular dynamic factorization algorithm for the simplex method. Math. Programming (1980) 18:49–61Crossref, Google Scholar
• McBride R. Solving embedded generalized network problems. Eur. J. Oper. Res. (1985) 21:82–92Crossref, Google Scholar
• McBride R. Progress in solving the multicommodity flow problem. SIAM J. Optim. (1998a) 8:947–955Crossref, Google Scholar
• McBride R. Advances in solving the multicommodity flow problem. Interfaces (1998b) 28:32–41Link, Google Scholar
• McBride R., Mamer J. Solving multicommodity flow problems with an embedded network simplex algorithm. INFORMS J. Comput. (1997) 9:154–163Link, Google Scholar
• Nazareth J.Computer Solution of Linear Programs (1987) (Oxford University Press, New York) Google Scholar
• Pinar M., Zenios S. Parallel decomposition of multicommodity network flows using a linear-quadratic penalty algorithm. ORSA J. Comput. (1992) 4:235–248Link, Google Scholar
• Schultz G., Meyer R. An interior point method for block angular optimization. SIAM J. Optim. (1991) 1:583–602Crossref, Google Scholar
• Zenios S., Pinar M., Dembo R. A smooth penalty function algorithm for network-structured problems. Eur. J. Oper. Res. (1995) 83:220–236Crossref, Google Scholar