Skip to main content
SpringerLink
Log in
Book cover

Linear Programming pp 303–318Cite as

A Path-Following Method

  • Chapter

  • 13k Accesses

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 114))

Abstract

In this chapter, we define an interior-point method for linear programming that is called a path-following method. Recall that for the simplex method we required a two-phase solution procedure. The path-following method is a one-phase method. This means that the method can begin from a point that is neither primal nor dual feasible and it will proceed from there directly to the optimal solution.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Kojima, M., Mizuno, S. & Yoshise, A. (1989), A primal-dual interior point algorithm for linear programming, in N. Megiddo, ed., ‘Progress in Mathematical Programming’, Springer-Verlag, New York, pp. 29–47.

    Google Scholar 

  • Lustig, I. (1990), ‘Feasibility issues in a primal-dual interior-point method for linear programming’, Mathematical Programming 49(2), 145–162.

    Article  MATH  MathSciNet  Google Scholar 

  • Khachian, L. (1979), ‘A polynomial algorithm in linear programming’, Doklady Academiia Nauk SSSR 244, 191–194. In Russian. English Translation: Soviet Mathematics Doklady 20: 191-194.

    Google Scholar 

  • Karmarkar, N. (1984), ‘A new polynomial time algorithm for linear programming’, Combinatorica 4, 373–395.

    Article  MATH  MathSciNet  Google Scholar 

  • Monteiro, R. & Adler, I. (1989), ‘Interior path following primal-dual algorithms: Part i: Linear programming’, Mathematical Programming 44, 27–41.

    Article  MATH  MathSciNet  Google Scholar 

  • Todd, M. (1995), Potential-reduction methods in mathematical programming, Technical Report 1112, SORIE, Cornell University, Ithaca, Ithaca.

    Google Scholar 

  • Anstreicher, K. (1996), Potential Reduction Algorithms, Technical report, Department of Management Sciences, University of Iowa.

    Google Scholar 

  • Wright, S. (1996), Primal-Dual Interior-Point Methods, SIAM, Philadelphia, USA.

    Google Scholar 

  • Nazareth, J. (1986), ‘Homotopy techniques in linear programming’, Algorithmica 1, 529–535.

    Article  MATH  MathSciNet  Google Scholar 

  • Nazareth, J. (1996), ‘The implementation of linear programming algorithms based on homotopies’, Algorithmica 15, 332–350.

    Article  MATH  MathSciNet  Google Scholar 

  • Carpenter, T., Lustig, I., Mulvey, J. & Shanno, D. (1993), ‘Higher order predictorcorrector interior point methods with application to quadratic objectives’, SIAM Journal on Optimization 3, 696–725.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Operations Research and Financial Engineering, Princeton University, New Jersey, USA

    Robert J. Vanderbei

Authors
  1. Robert J. Vanderbei
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Robert J.Vanderbei

About this chapter

Cite this chapter

Vanderbei, R.J. (2008). A Path-Following Method. In: Linear Programming. International Series in Operations Research & Management Science, vol 114. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74388-2_18

Download citation

Publish with us

Policies and ethics

Search

Navigation