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Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones

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Listed:
  • Jingyong Tang

    (Xinyang Normal University)

  • Jinchuan Zhou

    (Shandong University of Technology)

Abstract

In this paper we consider the nonlinear complementarity problem over circular cones (CCNCP) which contains a lot of circular cone optimization problems. We study a one-parametric class of smoothing functions which can be used to reformulate the CCNCP as a system of smooth nonlinear equations. Based on the equivalent reformulation, we propose a smoothing inexact Newton method to solve the CCNCP. In each iteration, the proposed method solves the nonlinear equations only approximately. Since the inexact direction is not necessarily descent, a new derivative-free nonmonotone line search is developed to ensure that the proposed method has global and local superlinear and quadratical convergence. Some numerical results are also reported.

Suggested Citation

  • Jingyong Tang & Jinchuan Zhou, 2020. "Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones," Annals of Operations Research, Springer, vol. 295(2), pages 787-808, December.
    • Handle: RePEc:spr:annopr:v:295:y:2020:i:2:d:10.1007_s10479-020-03773-8
    DOI: 10.1007/s10479-020-03773-8
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    References listed on IDEAS

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    1. Yasushi Narushima & Nobuko Sagara & Hideho Ogasawara, 2011. "A Smoothing Newton Method with Fischer-Burmeister Function for Second-Order Cone Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 79-101, April.
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    8. Xiao-Hong Liu & Zheng-Hai Huang, 2009. "A smoothing Newton algorithm based on a one-parametric class of smoothing functions for linear programming over symmetric cones," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 385-404, October.
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    Cited by:

    1. Jingyong Tang & Jinchuan Zhou & Hongchao Zhang, 2023. "An Accelerated Smoothing Newton Method with Cubic Convergence for Weighted Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 641-665, February.
    2. Jingyong Tang & Jinchuan Zhou & Zhongfeng Sun, 2023. "A derivative-free line search technique for Broyden-like method with applications to NCP, wLCP and SI," Annals of Operations Research, Springer, vol. 321(1), pages 541-564, February.

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