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

Author

Listed:
  • Sajad Fathi-Hafshejani

    (Shiraz University of Technology)

  • Alireza Fakharzadeh Jahromi

    (Shiraz University of Technology
    Fars Elites Foundation)

  • Mohammad Reza Peyghami

    (K. N. Toosi University of Technology)

  • Shengyuan Chen

    (York University)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:3:d:10.1007_s10957-018-1344-z
    DOI: 10.1007/s10957-018-1344-z
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    References listed on IDEAS

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    1. 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.
    2. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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