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An interior-point algorithm for \(P_*(\kappa )\)-LCP based on a new trigonometric kernel function with a double barrier term

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Abstract

In this paper, we present a new large-update interior-point algorithm for \(P_*(\kappa )\)-linear complementarity problem. The new algorithm is based on a trigonometric kernel function which differs from the existing kernel functions in which it has a double barrier term. By a simple analysis, we show that the new algorithm enjoys \({ O}((1+2\kappa )n^\frac{2}{3}\log \frac{n}{\varepsilon })\) iteration complexity. This complexity estimate improves a result from El Ghami et al. (Optim Theory Decis Mak Oper Res Appl 31: 331–349, 2013) and matches the currently best known complexity result for \(P_*(\kappa )\)-linear complementarity problem based on trigonometric kernel functions.

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Acknowledgments

The authors would like to deeply thank the referees for very valuable and helpful comments and suggestions, which made the paper more accurate and readable. This work was supported by the construction project of Guangxi key developing subject (Applied Mathematics (No. SXYB2015001) and the project of eduction and teaching reform of the higher education institutions of Hainan (No.439HNJG2014-90).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Guangxi Normal University for Nationalities, Chongzuo, 532200, People’s Republic of China

    Xin Li & Yan Chen

  2. College of Science, China Three Gorges University, Yichang, 443002, People’s Republic of China

    Mingwang Zhang

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  1. Xin Li
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  2. Mingwang Zhang
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  3. Yan Chen
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Correspondence to Xin Li.

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Li, X., Zhang, M. & Chen, Y. An interior-point algorithm for \(P_*(\kappa )\)-LCP based on a new trigonometric kernel function with a double barrier term. J. Appl. Math. Comput. 53, 487–506 (2017). https://doi.org/10.1007/s12190-015-0978-3

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  • DOI: https://doi.org/10.1007/s12190-015-0978-3

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