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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

Author

Listed:
  • Mousaab Bouafia

    (University of 8 May 1945 Guelma
    Normandie University)

  • Djamel Benterki

    (University Setif 1)

  • Adnan Yassine

    (Normandie University)

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.

Suggested Citation

  • Mousaab Bouafia & Djamel Benterki & Adnan Yassine, 2016. "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, Springer, vol. 170(2), pages 528-545, August.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-016-0895-0
    DOI: 10.1007/s10957-016-0895-0
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    Cited by:

    1. Sajad Fathi-Hafshejani & Alireza Fakharzadeh Jahromi & Mohammad Reza Peyghami & Shengyuan Chen, 2018. "Complexity of Interior Point Methods for a Class of Linear Complementarity Problems Using a Kernel Function with Trigonometric Growth Term," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 935-949, September.
    2. Fabio Vitor & Todd Easton, 2022. "Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming," Computational Optimization and Applications, Springer, vol. 83(1), pages 211-246, September.

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