Skip to main content
SpringerLink
Log in

A path-following version of the Todd-Burrell procedure for linear programming

  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

We propose a path-following version of the Todd-Burrell procedure to solve linear programming problems with an unknown optimal value. The path-following scheme is not restricted to Karmarkar's primal step; it can also be implemented with a dual Newton step or with a primal-dual step.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anstreicher K (1986) A monotonic projective algorithm for fractional linear programming. Algorithmica 1:483–498

    Google Scholar 

  2. de Ghellinck G, Vial J-P (1986) A polynomial Newton method for linear programming. Algorithmica 1:425–453

    Google Scholar 

  3. den Hertog D, Roos C (1991) A survey of search directions in interior point methods for linear programming. Mathematical Programming 52:481–509

    Google Scholar 

  4. Goffin J-L, Vial J-P (1994) Short steps with Karmarkar's projective algorithm for linear programming. SIAM Journal on Optimization 4:193–207

    Google Scholar 

  5. Karmarkar NK (1984) A new polynomial-time algorithm for linear programming. Combinatorica 4:373–395

    Google Scholar 

  6. Kojima M, Mizuno S, Yoshise A (1989) A primal-dual interior point algorithm for linear programming. In: Megiddo N (ed.) Progress in mathematical programming, interior point and related methods, Springer Verlag, New York, pp. 29–47

    Google Scholar 

  7. Monteiro RDC, Adler I (1989) Interior path following primal-dual algorithms, part I: Linear programming. Mathematical Programming 44:27–41

    Google Scholar 

  8. Renegar J (1988) A polynomial-time algorithm, based on Newton's method, for linear programming. Mathematical Programming 40:59–93

    Google Scholar 

  9. Shaw D, Goldfarb D (1994) A path-following projective interior point method for linear programming. SIAM J. Opt. 4:65–85

    Google Scholar 

  10. Todd MJ, Burrell BP (1986) An extension of Karmarkar's algorithm for linear programming using dual variables. Algorithmica 1:409–424

    Google Scholar 

  11. Vial J-P (1989) A unified approach to projective algorithms for linear programming. In: Dolecki S (ed.) Optimization, Lecture Notes in Mathematics, 1405, Springer Verlag, pp. 191–210

  12. Vial J-P (1996) A generic path-following algorithm with a sliding constraint and its application to linear programming and the computation of analytic centers. Technical Report 1996.8, LOGILAB/Management Studies, University of Geneva, Switzerland

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LOGILAB/Management Studies, University of Geneva, 102, Bd Carl-Vogt, CH-1211, Genève 4, Switzerland

    Jean-Philippe Vial

Authors
  1. Jean-Philippe Vial
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work has been completed with the support from the Fonds National Suisse de la Recherche Scientifique, grant 12-34002.92.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vial, JP. A path-following version of the Todd-Burrell procedure for linear programming. Mathematical Methods of Operations Research 46, 153–167 (1997). https://doi.org/10.1007/BF01217688

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01217688

Key words

Search

Navigation