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A full-Newton step feasible interior-point algorithm for \(P_*(\kappa )\)-linear complementarity problems

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Abstract

In this paper, a full-Newton step feasible interior-point algorithm is proposed for solving \(P_*(\kappa )\)-linear complementarity problems. We prove that the full-Newton step to the central path is local quadratically convergent and the proposed algorithm has polynomial iteration complexity, namely, \(O\left( (1+4\kappa )\sqrt{n}\log {\frac{n}{\varepsilon }}\right) \), which matches the currently best known iteration bound for \(P_*(\kappa )\)-linear complementarity problems. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm.

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Acknowledgments

The authors would like to thank the referees for their useful suggestions which improve the presentation of this paper. This research was supported by National Natural Science Foundation of China (No. 11001169), China Postdoctoral Science Foundation funded project (Nos. 2012T50427, 20100480604), Research Grant of Shanghai University of Engineering Science (No. 2013–21), Connotative Construction Project of Shanghai University of Engineering Science (No. NHKY-2012–13), and a Discovery Grant from the Australian Research Council.

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  1. College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, 201620, People’s Republic of China

    G. Q. Wang

  2. Department of Mathematics and Statistics, Curtin University, Perth, WA, 6845, Australia

    C. J. Yu & K. L. Teo

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  1. G. Q. Wang
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  2. C. J. Yu
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  3. K. L. Teo
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Correspondence to G. Q. Wang.

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Wang, G.Q., Yu, C.J. & Teo, K.L. A full-Newton step feasible interior-point algorithm for \(P_*(\kappa )\)-linear complementarity problems. J Glob Optim 59, 81–99 (2014). https://doi.org/10.1007/s10898-013-0090-x

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  • DOI: https://doi.org/10.1007/s10898-013-0090-x

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