Abstract
This chapter discusses some aspects of the computational comparison of the simplex method and the new interior point (barrier) methods for linear programming. In particular, we consider classes of problems with which the simplex method has traditionally had difficulty and present some computational results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
I. Adler, M. G. C. Resende, and G. Veiga, An implementation of Karmarkar’s algorithm for linear programming, Report ORC 86–8, Department of IE/OR, University of California, Berkeley (1986).
I. Adler, N. Karmarkar, M. G. C. Resende, and G. Veiga, An implementation of Karmarkar’s algorithm for linear programming, Presentation at the 22nd TIMS/ORSA meeting, Miami (1986).
M. Benichou, J. M. Gauthier, G. Hentges, and G. Ribière, The efficient solution of large-scale linear programming problems—some algorithmic techniques and computational results, Math. Programming 13 (1977), 280–322.
P. Boggs, K. Hoffman, and R. Jackson, NBS group report to MPS chairman, COAL Newslett., No. 13 (1985), 5–7.
H. P. Crowder, R. S. Dembo, and J. M. Mulvey, On reporting computational experiments with mathematical software, ACM Trans. Math. Software 5 (1979), 193–203.
J. J. H. Forrest and J. A. Tomlin, Updating triangular factors of the basis to maintain sparsity in the product form simplex method, Math. Programming 2 (1972), 263–278.
M. R. Garey and D. M. Gay, Letter from AT&T Bell Laboratories, COAL Newslett., No. 13 (1985), 3.
J. A. George and J. W. Liu, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs, N.J., 1981.
P. E. Gill, W. Murray, M. A. Saunders, J. A. Tomlin, and M. H. Wright, On projected Newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method, Math. Programming 36 (1986), 183–209.
D. Goldfarb and S. Mehrotra, A relaxed version of Karmarkar’s method, Math. Programming 40 (1988), 289–315.
E. Hellerman and D. C. Rarick, Reinversion with the partitioned preassigned pivot procedure, in Sparse Matrices and Their Applications, D. J. Rose and R. A. Willoughby (eds.), Plenum Press, New York, 1972, pp. 67–76.
A. J. Hoffman, M. Mannos, D. Sokolowsky, and N. Wiegmann, Computational experience in solving linear programs, SIAM J. 1 (1953), 1–33.
J. E. Kalan, Aspects of large-scale in-core linear programming, Proc. ACM Annual Conference, Chicago, ACM, New York, 1971, pp. 304–313.
N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984), 373–395.
N. Megiddo, Pathways to the optimal set in linear programming. In: Progress in Mathematical Programming: Interior-Point and Related Methods. Springer-Verlag, New York (1989).
B. A. Murtagh and M. A. Saunders, MINOS 5.0 User’s Guide, Report SOL 83–20, Department of Operations Research, Stanford University (1983).
J. Renegar, A polynomial-time algorithm, based on Newton’s method, for linear programming, Math. Programming 40 (1988), 59–93.
D. F. Shanno and R. E. Marsten, On implementing Karmarkar’s method, Working Paper 85–01, Graduate School of Administration, University of California, Davis (1985).
J. A. Tomlin, An experimental approach to Karmarkar’s projective method for linear programming, Math. Programming Studies 31 (1987), 175–191.
J. A. Tomlin and J. S. Welch, Formal optimization of some reduced linear programming problems, Math. Programming 27 (1983), 232–240.
J. A. Tomlin and J. S. Welch, Integration of a primal simplex network algorithm with a large-scale mathematical programming system, ACM Trans. Math. Software 11 (1985), 1–11.
J. A. Tomlin and J. S. Welch, Implementing an interior point method in a mathematical programming system, presented at the 22nd TIMS/ORSA meeting, Miami (1986).
Wall Street Journal, Karmarkar algorithm proves its worth, July 18, 1986.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Tomlin, J.A. (1989). A Note on Comparing Simplex and Interior Methods for Linear Programming. In: Megiddo, N. (eds) Progress in Mathematical Programming. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9617-8_6
Download citation
DOI: https://doi.org/10.1007/978-1-4613-9617-8_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-9619-2
Online ISBN: 978-1-4613-9617-8
eBook Packages: Springer Book Archive