Skip to main content
Book cover

Modelling, Computation and Optimization in Information Systems and Management Sciences pp 357–368Cite as

A Numerical Implementation of an Interior Point Methods for Linear Programming Based on a New Kernel Function

  • Conference paper

  • 1420 Accesses

Part of the Advances in Intelligent Systems and Computing book series (AISC,volume 359)

Abstract

In this paper, we define a new barrier function and propose a new primal-dual interior point methods based on this function for linear optimization. The proposed kernel function which yields a low algorithm complexity bound for both large and small-update interior point methods. This purpose is confirmed by numerical experiments showing the efficiency of our algorithm which are presented in the last of this paper.

Keywords

  • Linear Optimization
  • Kernel function
  • Interior Point methods
  • Complexity Bound

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-18161-5_30
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   169.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-18161-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   219.99
Price excludes VAT (USA)
Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersen, E.D., Gondzio, J., Meszaros, C., Xu, X.: Implementation of interior point methods for large scale linear programming. In: Terlaky, T. (ed.) Interior Point Methods of Mathematical Programming, pp. 189–252. Kluwer Academic Publisher, The Netherlands (1996)

    CrossRef  Google Scholar 

  2. Bai, Y.Q., El Ghami, M., Roos, C.: A new efficient large-update primal-dual interior point method based on a finite barrier. SIAM Journal on Optimization 13, 766–782 (2003)

    CrossRef  MATH  Google Scholar 

  3. Bai, Y.Q., El Ghami, M., Roos, C.: A comparative study of kernel functions for primal-dual interior point algorithms in linear optimization. SIAM Journal on Optimization 15, 101–128 (2004)

    CrossRef  MATH  MathSciNet  Google Scholar 

  4. Bai, Y.Q., Roos, C.: A primal-dual interior point method based on a new kernel function with linear growth rate. In: Proceedings of the 9th Australian Optimization Day, Perth, Australia (2002)

    Google Scholar 

  5. Bai, Y.Q., Roos, C.: A polynomial-time algorithm for linear optimization based on a new simple kernel function. Optimization Methods and Software 18, 631–646 (2003)

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. Bai, Y.Q., Guo, J., Roos, C.: A new kernel function yielding the best known iteration bounds for primal-dual interior point algorithms. Acta Mathematica Sinica 49, 259–270 (2007)

    Google Scholar 

  7. Cho, G.M.: An interior point algorithm for linear optimization based on a new barrier function. Applied Mathematics and Computation 218, 386–395 (2011)

    CrossRef  MATH  MathSciNet  Google Scholar 

  8. El Ghami, M., Guennoun, Z.A., Bouali, S., Steihaug, T.: Interior point methods for linear optimization based on a kernel function with a trigonometric barrier term. Journal of Computational and Applied Mathematics 236, 3613–3623 (2012)

    CrossRef  MATH  MathSciNet  Google Scholar 

  9. El Ghami, M., Ivanov, I., Melissen, J.B.M., Roos, C., Steihaug, T.: A polynomial-time algorithm for linear optimization based on a new class of kernel functions. Journal of Computational and applied Mathematics 224, 500–513 (2009)

    CrossRef  MATH  MathSciNet  Google Scholar 

  10. El Ghami, M., Roos, C.: Generic primal-dual interior point methods based on a new kernel function. RAIRO-Operations Research 42, 199–213 (2008)

    CrossRef  MATH  MathSciNet  Google Scholar 

  11. Gonzaga, C.C.: Path following methods for linear programming. SIAM Review 34, 167–227 (1992)

    CrossRef  MATH  MathSciNet  Google Scholar 

  12. den Hertog, D.: Interior point approach to linear, quadratic and convex programming. Mathematical Application, vol. 277. Kluwer Academic Publishers, Dordrecht (1994)

    CrossRef  MATH  Google Scholar 

  13. Karmarkar, N.K.: A new polynomial-time algorithm for linear programming. In: Proceedings of the 16th Annual ACM Symposium on Theory of Computing, vol. 4, pp. 373–395 (1984)

    Google Scholar 

  14. Peng, J., Roos, C., Terlaky, T.: Self-regular functions and new search directions for linear and semidefinite optimization. Mathematical Programming 93, 129–171 (2002)

    CrossRef  MATH  MathSciNet  Google Scholar 

  15. Peng, J., Roos, C., Terlaky, T.: Self-Regularity: A New Paradigm for Primal-Dual interior point Algorithms. Princeton University Press, Princeton (2002)

    Google Scholar 

  16. Roos, C., Terlaky, T., Vial, J.P.: Theory and algorithms for linear optimization. In: An Interior Point Approach. John Wiley & Sons, Chichester (1997)

    Google Scholar 

  17. Ye, Y.: Interior point algorithms. Theory and Analysis. John-Wiley & Sons, Chichester (1997)

    CrossRef  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LabCAV, Laboratoire de Contrôle Avancé, Université de Guelma, Guelma, Algérie

    Mousaab Bouafia

  2. LMFN, Laboratoire de Mathématiques Fondamentales et Numériques, Sétif-1, Algérie

    Djamel Benterki

  3. LMAH, Laboratoire de Mathématiques Appliquées du Havre, Université du Havre, Le Havre, France

    Adnan Yassine

Authors
  1. Mousaab Bouafia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Djamel Benterki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Adnan Yassine
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mousaab Bouafia .

Editor information

Editors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science, University of Lorraine-Metz, Metz, France

    Hoai An Le Thi

  2. Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, Rouen, France

    Tao Pham Dinh

  3. Division of Knowledge Management Systems Institute of Informatics (I-32), Wroclaw University of Technology, Wroclaw, Poland

    Ngoc Thanh Nguyen

Rights and permissions

Reprints and Permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Bouafia, M., Benterki, D., Yassine, A. (2015). A Numerical Implementation of an Interior Point Methods for Linear Programming Based on a New Kernel Function. In: Le Thi, H., Pham Dinh, T., Nguyen, N. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. Advances in Intelligent Systems and Computing, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-319-18161-5_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-18161-5_30

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18160-8

  • Online ISBN: 978-3-319-18161-5

  • eBook Packages: EngineeringEngineering (R0)