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A new full-Newton step interior-point method for \(P_{*}(\kappa )\)-LCP based on a positive-asymptotic kernel function

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A Correction to this article was published on 11 February 2021

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Abstract

In this paper, we propose a new full-Newton step interior-point method (IPM) for \(P_{*}(\kappa )\) linear complementarity problem (LCP). The search direction is obtained by applying algebraic equivalent transformation on the centering equation of the central path which is introduced by Darvay et al. for linear optimization (Optim Lett 12(5):1099–1116, 2018). They point out that the search direction can also be obtained by using a positive-asymptotic kernel function. This kernel function has not been used in the complexity analysis of IPMs for \(P_{*}(\kappa )\)-LCP before. Assuming a strictly feasible starting point is available, we show that the algorithm has the iteration complexity bound \(O((1+4\kappa )\sqrt{n}\log {\frac{n}{\epsilon }})\), which is the best known complexity result for such methods. Some numerical results have been provided.

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Authors and Affiliations

  1. Three Gorges Mathematical Research Center, China Three Gorges University, Yi Chang, 443002, China

    Mingwang Zhang, Kun Huang, Mengmeng Li & Yanli Lv

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  1. Mingwang Zhang
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  2. Kun Huang
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  4. Yanli Lv
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Correspondence to Kun Huang.

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Supported by National Natural Science Foundation of China (Grant No. 1217180)

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Zhang, M., Huang, K., Li, M. et al. A new full-Newton step interior-point method for \(P_{*}(\kappa )\)-LCP based on a positive-asymptotic kernel function. J. Appl. Math. Comput. 64, 313–330 (2020). https://doi.org/10.1007/s12190-020-01356-1

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  • DOI: https://doi.org/10.1007/s12190-020-01356-1

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