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A nonmonotone smoothing Newton method for system of nonlinear inequalities based on a new smoothing function

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Abstract

In this paper, a nonmonotone smoothing Newton method is proposed for solving system of nonlinear inequalities. By constructing a new smoothing function, the problem is approximated via a family of parameterized smooth equations \(H_u(z)=0\). A smoothing Newton method is developed for solving the system of nonlinear inequalities by adopting a new nonmonotone line search scheme. Under mild assumptions, our algorithm is shown to possess global and local quadratic convergence properties. Some preliminary numerical results are reported.

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Authors and Affiliations

  1. College of Science, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, People’s Republic of China

    Yuan Liuyang, Cui Fei & Wang Wenbo

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, People’s Republic of China

    Wan Zhongping

  3. School of Information Science and Engineering, University of Science and Technology, Wuhan, 430081, Hubei, People’s Republic of China

    Li Weigang

Authors
  1. Yuan Liuyang
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  2. Cui Fei
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  3. Wan Zhongping
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  4. Li Weigang
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  5. Wang Wenbo
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Corresponding author

Correspondence to Yuan Liuyang.

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Communicated by Jinyun Yuan.

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This paper is supported by the National Natural Science Foundation of China (Nos.11401450, 11861026, 11871383, 61671338)

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Liuyang, Y., Fei, C., Zhongping, W. et al. A nonmonotone smoothing Newton method for system of nonlinear inequalities based on a new smoothing function. Comp. Appl. Math. 38, 91 (2019). https://doi.org/10.1007/s40314-019-0856-y

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  • DOI: https://doi.org/10.1007/s40314-019-0856-y

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