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Complexity of Interior Point Methods for a Class of Linear Complementarity Problems Using a Kernel Function with Trigonometric Growth Term

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Abstract

In this paper, we propose a large-update primal-dual interior point method for solving a class of linear complementarity problems based on a new kernel function. The main aspects distinguishing our proposed kernel function from the others are as follows: Firstly, it incorporates a specific trigonometric function in its growth term, and secondly, the corresponding barrier term takes finite values at the boundary of the feasible region. We show that, by resorting to relatively simple techniques, the primal-dual interior point methods designed for a specific class of linear complementarity problems enjoy the so-called best-known iteration complexity for the large-update methods.

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Acknowledgements

The authors would like to thank the research councils of Shiraz University of Technology, K.N. Toosi University of Technology and York University for supporting this work. The authors would also like to thank M. Ataei for his helpful comments on the paper.

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Authors and Affiliations

  1. Faculty of Mathematics, Shiraz University of Technology, P.O.Box 71555-313, Shiraz, Iran

    Sajad Fathi-Hafshejani & Alireza Fakharzadeh Jahromi

  2. Fars Elites Foundation, P.O. Box 71966-98893, Shiraz, Iran

    Alireza Fakharzadeh Jahromi

  3. Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran

    Mohammad Reza Peyghami

  4. Department of Mathematics and Statistics, York University, Toronto, ON, Canada

    Shengyuan Chen

Authors
  1. Sajad Fathi-Hafshejani
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  2. Alireza Fakharzadeh Jahromi
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  3. Mohammad Reza Peyghami
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  4. Shengyuan Chen
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Corresponding author

Correspondence to Sajad Fathi-Hafshejani.

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Communicated by Yurii Nesterov.

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Fathi-Hafshejani, S., Fakharzadeh Jahromi, A., Peyghami, M.R. et al. Complexity of Interior Point Methods for a Class of Linear Complementarity Problems Using a Kernel Function with Trigonometric Growth Term. J Optim Theory Appl 178, 935–949 (2018). https://doi.org/10.1007/s10957-018-1344-z

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  • DOI: https://doi.org/10.1007/s10957-018-1344-z

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