A Levenberg–Marquardt Method for Nonlinear Complementarity Problems Based on Nonmonotone Trust Region and Line Search Techniques

  • Bin Fan
  • Changfeng Ma
  • Aidi Wu
  • Chao Wu


Using the FB function, we propose a new Levenberg–Marquardt algorithm for nonlinear complementarity problem. To obtain the global convergence, the algorithm uses the nonmonotone trust region and line search techniques under a convenient boundedness assumption. Furthermore, we get local superlinear/quadratic convergence of the algorithm under a nonsingularity condition. Some numerical examples are given to illustrate the performance and efficiency of the presented algorithm.


Nonlinear complementarity problems nonmonotone Levenberg–Marquardt algorithm trust region technique global convergence superlinear/quadratic convergence 

Mathematics Subject Classification

65K05 90C33 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and InformaticsFujian Normal UniversityFuzhouPeople’s Republic of China
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China
  3. 3.College of Computer and Information SciencesFujian Agriculture and Forestry UniversityFuzhouPeople’s Republic of China
  4. 4.School of Electronics and Information EngineeringFuqing Branch of Fujian Normal UniversityFuqingPeople’s Republic of China

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