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A Nonsmooth L-M Method for Solving the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone

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Abstract

In this paper the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone is reformulated as a system of nonsmooth equations. Based on this reformulation, the famous Levenberg-Marquardt (L-M) algorithm is employed to obtain its solution. Theoretical results that relate the stationary points of the merit function to the solution of the GNCP are presented. Under mild assumptions, we show that the L-M algorithm is both globally and superlinearly convergent. Moreover, a method to calculate a generalized Jacobian is given and numerical experimental results are presented.

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Authors and Affiliations

  1. Institute of Operations Research, Qufu Normal University, Rizhao Shandong 276800 , People’s Republic of China

    Yiju Wang, Fengming Ma & Jianzhong Zhang

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

    Yiju Wang

Authors
  1. Yiju Wang
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  2. Fengming Ma
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  3. Jianzhong Zhang
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Correspondence to Yiju Wang, Fengming Ma or Jianzhong Zhang.

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Wang, Y., Ma, F. & Zhang, J. A Nonsmooth L-M Method for Solving the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone. Appl Math Optim 52, 73–92 (2005). https://doi.org/10.1007/s00245-005-0823-4

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  • DOI: https://doi.org/10.1007/s00245-005-0823-4

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