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A nonmonotone Jacobian smoothing inexact Newton method for NCP

Author

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  • Sanja Rapajić

    (University of Novi Sad)

  • Zoltan Papp

    (University of Novi Sad)

Abstract

In this paper we propose Jacobian smoothing inexact Newton method for nonlinear complementarity problems (NCP) with derivative-free nonmonotone line search. This nonmonotone line search technique ensures globalization and is a combination of Grippo-Lampariello-Lucidi (GLL) and Li-Fukushima (LF) strategies, with the aim to take into account their advantages. The method is based on very well known Fischer-Burmeister reformulation of NCP and its smoothing Kanzow’s approximation. The mixed Newton equation, which combines the semismooth function with the Jacobian of its smooth operator, is solved approximately in every iteration, so the method belongs to the class of Jacobian smoothing inexact Newton methods. The inexact search direction is not in general a descent direction and this is the reason why nonmonotone scheme is used for globalization. Global convergence and local superlinear convergence of method are proved. Numerical performances are also analyzed and point out that high level of nonmonotonicity of this line search rule enables robust and efficient method.

Suggested Citation

  • Sanja Rapajić & Zoltan Papp, 2017. "A nonmonotone Jacobian smoothing inexact Newton method for NCP," Computational Optimization and Applications, Springer, vol. 66(3), pages 507-532, April.
    • Handle: RePEc:spr:coopap:v:66:y:2017:i:3:d:10.1007_s10589-016-9881-6
    DOI: 10.1007/s10589-016-9881-6
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    References listed on IDEAS

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    1. Changfeng Ma, 2010. "A new smoothing and regularization Newton method for P 0 -NCP," Journal of Global Optimization, Springer, vol. 48(2), pages 241-261, October.
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    3. Bilian Chen & Changfeng Ma, 2011. "A new smoothing Broyden-like method for solving nonlinear complementarity problem with a P 0 -function," Journal of Global Optimization, Springer, vol. 51(3), pages 473-495, November.
    4. Dong-Hui Li & Masao Fukushima, 2001. "Globally Convergent Broyden-Like Methods for Semismooth Equations and Applications to VIP, NCP and MCP," Annals of Operations Research, Springer, vol. 103(1), pages 71-97, March.
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