Skip to main content

Implementation Issues

  • Chapter
  • First Online:
Linear Programming

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 285))

  • 11k Accesses

Abstract

In the previous chapter, we rewrote the simplex method using matrix notation. This is the first step toward our aim of describing the simplex method as one would implement it as a computer program. In this chapter, we shall continue in this direction by addressing some important implementation issues.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Occasionally we use the superscript − T for the transpose of the inverse of a matrix. Hence, E −T = (E −1)T.

References

  • Dantzig, G., & Orchard-Hayes, W. (1954). The product form for the inverse in the simplex method. Mathematical Tables and Other Aids to Computation, 8, 64–67.

    Article  Google Scholar 

  • Duff, I., Erisman, A., & Reid, J. (1986). Direct methods for sparse matrices. Oxford: Oxford University Press.

    Google Scholar 

  • Forrest, J., & Tomlin, J. (1972). Updating triangular factors of the basis to maintain sparsity in the product form simplex method. Mathematical Programming, 2, 263–278.

    Article  Google Scholar 

  • Gill, P., Murray, W., & Wright, M. (1991). Numerical linear algebra and optimization (Vol. 1). Redwood City: Addison-Wesley.

    Google Scholar 

  • Goldfarb, D., & Reid, J. (1977). A practicable steepest-edge simplex algorithm. Mathematical Programming, 12, 361–371.

    Article  Google Scholar 

  • Golub, G., & VanLoan, C. (1989). Matrix computations (2nd ed.). Baltimore: The Johns Hopkins University Press.

    Google Scholar 

  • Harris, P. (1973). Pivot selection methods of the Devex LP code. Mathematical Programming, 5, 1–28.

    Article  Google Scholar 

  • Markowitz, H. (1957). The elimination form of the inverse and its application to linear programming. Management Science, 3, 255–269.

    Article  Google Scholar 

  • Reid, J. (1982). A sparsity-exploiting variant of the Bartels-Golub decomposition for linear programming bases. Mathematical Programming, 24, 55–69.

    Article  Google Scholar 

  • Saunders, M. (1973). The complexity of LU updating in the simplex method. In R. Andersen, & R. Brent (Eds.), The complexity of computational problem solving (pp. 214–230). Brisbane: University of Queensland Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Vanderbei, R.J. (2020). Implementation Issues. In: Linear Programming. International Series in Operations Research & Management Science, vol 285. Springer, Cham. https://doi.org/10.1007/978-3-030-39415-8_8

Download citation

Publish with us

Policies and ethics