Skip to main content

Linear Programming Algorithms

  • Chapter
  • First Online:

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 127))

Abstract

LPs can be formulated in various forms. An LP problem consists of the objective function, the constraints, and the decision variables. This chapter presents the theoretical background of LP. More specifically, the different formulations of the LP problem are presented. Detailed steps on how to formulate an LP problem are given. In addition, the geometry of the feasible region and the duality principle are also covered. Finally, a brief description of LP algorithms that will be used in this book is also presented.

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

Change history

  • 11 January 2018

    The original version of the book was inadvertently published without updating the following corrections:

References

  1. Dantzig, G. B. (1953). Computational algorithm of the revised simplex method. RAND Report RM-1266, The RAND Corporation, Santa Monica, CA.

    Google Scholar 

  2. Lemke, C. E. (1954). The dual method of solving the linear programming problem. Naval Research Logistics Quarterly, 1(1), 36–47.

    Article  MathSciNet  Google Scholar 

  3. MathWorks. (2017). MuPAD: user’s guide. Available online at: http://cn.mathworks.com/help/pdf_doc/symbolic/mupad_ug.pdf (Last access on March 31, 2017).

  4. Mehrotra, S. (1992). On the implementation of a primal-dual interior point method. SIAM Journal on Optimization, 2, 575–601.

    Article  MathSciNet  Google Scholar 

  5. Paparrizos, K. (1991). An infeasible exterior point simplex algorithm for assignment problems. Mathematical Programming, 51(1–3), 45–54.

    Article  MathSciNet  Google Scholar 

  6. Paparrizos, K. (1993). An exterior point simplex algorithm for (general) linear programming problems. Annals of Operations Research, 47, 497–508.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

2.1 Electronic Supplementary Material

Below is the link to the electronic supplementary material.

Chapter 2 (Zip 15 kb)

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ploskas, N., Samaras, N. (2017). Linear Programming Algorithms. In: Linear Programming Using MATLAB® . Springer Optimization and Its Applications, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-319-65919-0_2

Download citation

Publish with us

Policies and ethics