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An experimental approach to karmarkar’s projective method for linear programming

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Computation Mathematical Programming

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 31))

Abstract

This paper describes the evolution of an experimental implementation of the Karmarkar projective method and gives computational results for some small to medium, but realistically structured models.

This paper supersedes an earlier version entitled “An Experimental Approach to Karmarkar’s Linear Programming Algorithm.”

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References

  1. M. Benichou, L.M. Gauthier, G. Hentges and G. Ribiere, “The efficient solution of large-scale linear programming problems—Some algorithmic techniques and computational results,” Mathematical Programming 13 (1977) 280–322.

    Article  MATH  MathSciNet  Google Scholar 

  2. G.B. Dantzig, Linear programming and extensions (Princeton University Press, Princeton, NJ, 1963).

    MATH  Google Scholar 

  3. A. George and M.T. Heath, “Solution of sparse linear least squares problems using Givens rotations,” Linear Algebra and its Applications 34 (1980) 69–83.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. George and J.W.-H. Liu, Computer solution of large sparse positive definite systems (Prentice-Hall, Englewood Cliffs, NJ, 1981).

    MATH  Google Scholar 

  5. A. George and E. Ng, “A new release of SPARSPAK—The Waterloo sparse matrix package,” ACM SIGNUM Newsletter 19, number 4 (1984) 9–13.

    Article  MathSciNet  Google Scholar 

  6. P.E. Gill, W. Murray and M.H. Wright, Practical optimization (Academic Press, London, 1981).

    MATH  Google Scholar 

  7. G.H. Golub and C.F. Van Loan, Matrix computations (Johns Hopkins University Press, Baltimore, MD, 1983).

    MATH  Google Scholar 

  8. M.T. Heath, “Numerical methods for large sparse linear least squares problems,” SIAM Journal on Scientific and Statistical Computing 5 (1984) 497–513.

    Article  MATH  MathSciNet  Google Scholar 

  9. IBM Corporation, “Mathematical programming system/360, Version 2, System Manual,” Form Y20-0065-2 (White Plains, NY, 1969).

    Google Scholar 

  10. N. Karmarkar, “A new polynomial-time algorithm for linear programming,” Combinatorica 4 (1984) 373–395.

    Article  MATH  MathSciNet  Google Scholar 

  11. N. Karmarkar, Seminar presentations at the 18th joint ORSA/TIMS national meeting (Dallas, TX, November 1984) and at Stanford University (Stanford, CA, January, 1985).

    Google Scholar 

  12. Ketron, Inc., “MPSIII users manual,” Revision 11 (Arlington, VA, June, 1984).

    Google Scholar 

  13. G. Kolata, “A fast way to solve hard problems,” Science 225 (1984) 1379–1380.

    Article  Google Scholar 

  14. C.C. Paige and M.A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” ACM Transactions on Mathematical Software 8 (1982) 43–71.

    Article  MATH  MathSciNet  Google Scholar 

  15. M. Saiidi and J.A. Tomlin, “Some computational experiments with Scolnik’s linear programming approach,” SIGMAP Newsletter 18 (1975) 30–37.

    Google Scholar 

  16. M.A. Saunders, “Large scale linear programming using the Cholesky factorization,” Technical Report STAN-CS-72-252, Computer Science Department, Stanford University (Stanford, CA, 1972).

    Google Scholar 

  17. J.A. Tomlin and J.S. Welch, “Formal optimization of some reduced linear programming problems,” Mathematical Programming 27 (1983) 232–240.

    Article  MATH  MathSciNet  Google Scholar 

  18. J.A. Tomlin and J.S. Welch, “Integration of a primal simplex algorithm with a large scale mathematical programming system,” ACM Transactions on Mathematical Software 11 (1985) 1–11.

    Article  MathSciNet  Google Scholar 

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K. L. Hoffman R. H. F. Jackson J. Telgen

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© 1987 The Mathematical Programming Society, Inc.

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Tomlin, J.A. (1987). An experimental approach to karmarkar’s projective method for linear programming. In: Hoffman, K.L., Jackson, R.H.F., Telgen, J. (eds) Computation Mathematical Programming. Mathematical Programming Studies, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121187

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  • DOI: https://doi.org/10.1007/BFb0121187

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00932-7

  • Online ISBN: 978-3-642-00933-4

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