Solving Real-World Linear Programs: A Decade and More of Progress

References

  • Applegate D., Bixby R., Chvátal V., Cook W.Solving Traveling Salesman ProblemsForthcomingGoogle Scholar
  • Bixby R. E. Commentary: Progress in linear programming. ORSA J. Comput. (1994) 6:15–22LinkGoogle Scholar
  • Brearley A. L., Mitra G., Williams H. P. Analysis of mathematical programming problems prior to applying the simplex algorithm. Math. Programming (1975) 8:54–83CrossrefGoogle Scholar
  • Carolan W. J., Hill J. E., Kennington J. L., Niemi S., Wichmann S. J. An empirical evaluation of the KORBX algorithms for military airlift applications. Oper. Res. (1990) 38(2):240–248LinkGoogle Scholar
  • Castro J. A specialized interior-point algorithm for multicommodity network flows. SIAM J. Optim. (2000) 10(3):852–877CrossrefGoogle Scholar
  • Chvátal V.Linear Programming (1983) (Freeman, New York) Google Scholar
  • Dantzig G. Programming in a linear structure. (1948) (U.S. Air Force Comptroller, USAF, Washington, D.C.) Google Scholar
  • Dantzig G.Linear Programming and Extensions (1963) (Princeton University Press, Princeton, NJ) CrossrefGoogle Scholar
  • Forrest J. J., Goldfarb D. Steepest-edge simplex algorithms for linear programming. Math. Programming (1992) 57:341–374CrossrefGoogle Scholar
  • Gass S. I. The first linear-programming shoppe. Oper. Res. (2002) 50:61–68LinkGoogle Scholar
  • Gilbert J. R., Peierls T. Sparse partial pivoting in time proportional to arithmetic operations. SIAM J. Sci. Statist. Comput. (1988) 9:862–874CrossrefGoogle Scholar
  • Goldfarb D. Using the steepest-edge simplex algorithm to solve sparse linear programs. Sparse Matrix Computations (1976) (Academic Press)227–240CrossrefGoogle Scholar
  • Grötschel M., Holland O. Solution of large-scale symmetric travelling salesman problems. Math. Programming (1991) 51:141–202CrossrefGoogle Scholar
  • Harris P. M. J. Pivot selection methods of the devex LP code. Math. Programming (1974) 5:1–28CrossrefGoogle Scholar
  • Hellerman E., Rarick D. Reinversion with the preassigned pivot procedure. Math. Programming (1971) 1:195–216CrossrefGoogle Scholar
  • Hoffman A., Mannos M., Sokolowsky D., Wiegmann D. Computational experience in solving linear programs. SIAM J. (1953) 1:1–33Google Scholar
  • Kalan J. E. Aspects of large-scale in-core linear programming. Proc. ACM Conf. (1971) Chicago, IL:304–313CrossrefGoogle Scholar
  • Karmarkar N. A new polynomial-time algorithm for linear programming. Combinatorica (1984) 4:373–395CrossrefGoogle Scholar
  • Lemke C. E. The dual method of solving the linear programming problem. Naval Res. Logist. Quart. (1954) 1:36–47CrossrefGoogle Scholar
  • Lustig I. J., Marsten R., Shanno D. F. Interior point methods for linear programming: Computational state of the art. ORSA J. Comput. (1994) 6(1):1–14LinkGoogle Scholar
  • Marsten R. E. XMP: A structured library of subroutines for experimental mathematical programming. ACM Trans. Math. Software (1981) 7:481–497CrossrefGoogle Scholar
  • Murtagh B. A., Saunders M. A.MINOS 5.5 User's Guide (1998) . Report SOL 83-20R, Dept of Operations Research, Stanford University, Stanford, CAGoogle Scholar
  • Orchard-Hays W. History of the development of LP solvers. Interfaces (1990) 20(4):61–73LinkGoogle Scholar
  • Orden A. Solution of systems of linear inequalities on a digital computer. Proc. ACM. (1952) CrossrefGoogle Scholar
  • Rothberg E., Hendrickson B. Sparse matrix ordering methods for interior point linear programming. INFORMS J. Comput. (1998) 10(1):107–113LinkGoogle Scholar
  • Stigler G. J. The cost of subsistence. J. Farm Econom. (1945) 27(2):303–314CrossrefGoogle Scholar
  • Suhl U. H., Suhl L. M. Computing sparse LU factorizations for large-scale linear programming bases. ORSA J. Comput. (1990) 2:325–335LinkGoogle Scholar
  • Wright S. J.Primal-Dual Interior-Point Methods (1997) (SIAM, Philadelphia, PA) CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.