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An Efficient Primal–Dual Interior Point Method for Linear Programming Problems Based on a New Kernel Function with a Trigonometric Barrier Term

Journal of Optimization Theory and Applications volume 170, pages 528–545 (2016)Cite this article

Abstract

In this paper, we present a primal–dual interior point method for linear optimization problems based on a new efficient kernel function with a trigonometric barrier term. We derive the complexity bounds for large and small-update methods, respectively. We obtain the best known complexity bound for large update, which improves significantly the so far obtained complexity results based on a trigonometric kernel function given by Peyghami et al. The results obtained in this paper are the first to reach this goal.

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Acknowledgments

The authors are very grateful and would like to thank the anonymous referees for their suggestions and helpful comments, which significantly improved the presentation of this paper.

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Authors and Affiliations

  1. LabCAV, Laboratory of Advanced Control, University of 8 May 1945 Guelma, BP 401, 24000, Guelma, Algeria

    Mousaab Bouafia

  2. LMAH - ULH, FR CNRS 3335, Normandie University, 25 rue Philippe Lebon, 76600, Le Havre, France

    Mousaab Bouafia & Adnan Yassine

  3. LMFN, Laboratory of Fundamental and Numerical Mathematics, University Setif 1, 19000, Sétif, Algeria

    Djamel Benterki

Authors
  1. Mousaab Bouafia
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  2. Djamel Benterki
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  3. Adnan Yassine
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Correspondence to Mousaab Bouafia.

Additional information

Communicated by Suliman Saleh Al-Homidan.

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Bouafia, M., Benterki, D. & Yassine, A. An Efficient Primal–Dual Interior Point Method for Linear Programming Problems Based on a New Kernel Function with a Trigonometric Barrier Term. J Optim Theory Appl 170, 528–545 (2016). https://doi.org/10.1007/s10957-016-0895-0

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  • DOI: https://doi.org/10.1007/s10957-016-0895-0

Keywords

  • Linear optimization
  • Kernel function
  • Interior point methods
  • Complexity bound

Mathematics Subject Classification

  • 90C05
  • 90C31
  • 90C51