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An efficient twice parameterized trigonometric kernel function for linear optimization

  • Mousaab BouafiaEmail author
  • Adnan Yassine
Research Article
  • 41 Downloads

Abstract

Recently, Bouafia et al. (J Optim Theory Appl 170:528–545, 2016) investigated a new efficient kernel function that differs from self-regular kernel functions. The kernel function has a trigonometric barrier term. This paper introduces a new efficient twice parametric kernel function that combines the parametric classic function with the parametric kernel function trigonometric barrier term given by Bouafia et al. (J Optim Theory Appl 170:528–545, 2016) to develop primal–dual interior-point algorithms for solving linear programming problems. In addition, we obtain the best complexity bound for large and small-update primal–dual interior point methods. This complexity estimate improves results obtained in Li and Zhang (Oper Res Lett 43(5):471–475, 2015), Peyghami and Hafshejani (Numer Algorithms 67:33–48, 2014) and matches the best bound obtained in Bai et al. (J Glob Optim 54:353–366) and Peng et al. (J Comput Technol 6:61–80, 2001). Finally, our numerical experiments on some test problems confirm that the new kernel function has promising applications compared to the kernel function given by Fathi-Hafshejani (Optimization 67(10):1605–1630, 2018).

Keywords

Linear optimization Kernel function Interior point methods Complexity bound 

Mathematics Subject Classification

90C05 90C31 90C51 

Notes

Acknowledgements

We thank an anonymous referee for comments that helped us improve the readability of this paper. I dedicate my work to my mother, Fatima Zohra SANSRI, who has been a constant source of love and encouragement.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of 8 May 1945 GuelmaGuelmaAlgeria
  2. 2.UNIHAVRE, LMAH, FR-CNRS-3335, ISCNNormandie UniversityLe HavreFrance

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