An interior-point method for \(P_*(\kappa )\)-linear complementarity problem based on a trigonometric kernel function

Abstract

Recently, El Ghami (Optim Theory Decis Mak Oper Res Appl 31:331–349, 2013) proposed a primal dual interior point method for \(P_*(\kappa )\)-Linear Complementarity Problem (LCP) based on a trigonometric barrier term and obtained the worst case iteration complexity as \(O\left( (1+2\kappa )n^{\frac{3}{4}}\log \frac{n}{\epsilon }\right) \) for large-update methods. In this paper, we present a large update primal–dual interior point algorithm for \(P_{*}(\kappa )\)-LCP based on a new trigonometric kernel function. By a simple analysis, we show that our algorithm based on the new kernel function enjoys the worst case \(O\left( (1+2\kappa )\sqrt{n}\log n\log \frac{n}{\epsilon }\right) \) iteration bound for solving \(P_*(\kappa )\)-LCP. This result improves the worst case iteration bound obtained by El Ghami for \(P_*(\kappa )\)-LCP based on trigonometric kernel functions significantly.

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Acknowledgments

The authors would like to thank the Research Council of K.N. Toosi University of Technology for supporting the work.

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Correspondence to M. Reza Peyghami.

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Hafshejani, S.F., Fatemi, M. & Peyghami, M.R. An interior-point method for \(P_*(\kappa )\)-linear complementarity problem based on a trigonometric kernel function. J. Appl. Math. Comput. 48, 111–128 (2015). https://doi.org/10.1007/s12190-014-0794-1

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Keywords

  • Kernel function
  • \(P_*(\kappa )\)-linear complementarity problem
  • Primal–dual interior point methods
  • Large-update methods

Mathematical Subject Classification (2010)

  • 90C05
  • 90C51