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A derivative-free line search technique for Broyden-like method with applications to NCP, wLCP and SI

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Abstract

We propose a new derivative-free line search technique which contains the classical Li-Fukushima derivative-free line search [Optim. Methods Softw. 13 (3), 181–201, 2000] as a special case. The new line search can enable us to choose a larger step size at each iteration and reduce the number of function evaluations at each step. Based on the new line search, we prove that Broyden-like method for solving the nonlinear equation is globally and locally superlinearly convergent under appropriate assumptions. Moreover, we present some nonlinear equations arising from nonlinear complementarity problems (NCP), weighted linear complementarity problems (wLCP) and system of inequalities (SI). Numerical results show that Broyden-like method based on the new line search has better numerical performance than that based on Li-Fukushima line search.

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Acknowledgements

Research of this paper was partly supported by National Natural Science Foundation of China (11771255), Young Innovation Teams of Shandong Province (2019KJI013), Natural Science Foundation of Henan Province (222300420520) and Key scientific research projects of Higher Education of Henan Province (22A110020). We are very grateful to the two referees for their valuable comments on the paper which have considerably improved the paper.

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  1. School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, China

    Jingyong Tang

  2. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255049, China

    Jinchuan Zhou & Zhongfeng Sun

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  1. Jingyong Tang
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  2. Jinchuan Zhou
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Tang, J., Zhou, J. & Sun, Z. A derivative-free line search technique for Broyden-like method with applications to NCP, wLCP and SI. Ann Oper Res 321, 541–564 (2023). https://doi.org/10.1007/s10479-022-04796-z

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