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Calcolo

, 55:37 | Cite as

The modulus-based nonsmooth Newton’s method for solving a class of nonlinear complementarity problems of P-matrices

  • Hua Zheng
  • Seakweng Vong
Article

Abstract

By applying the Newton’s iteration to the equivalent modulus equations of the nonlinear complementarity problems of P-matrices, a modulus-based nonsmooth Newton’s method is established. The nearly quadratic convergence of the new method is proved under some assumptions. The strategy of choosing the initial iteration vector is given, which leads to a modified method. Numerical examples show that the new methods have higher convergence precision and faster convergence rate than the known modulus-based matrix splitting iteration method.

Keywords

Nonlinear complementarity problem Modulus-based method Nonsmooth Newton’s method P-matrix 

Mathematics Subject Classification

90C33 65F10 

Notes

Acknowledgements

The authors would like to thank the referee for the helpful comments. The work was supported by the National Natural Science Foundation of China (Grant No. 11601340), University of Macau (Grant No. MYRG2017-00098-FST), Macao Science and Technology Development Fund (Grant No. 050/2017/A), the Opening Project of Guangdong Provincial Engineering Technology Research Center for Data Sciences(Grant No. 2016KF11) and Science and Technology Planning Project of Shaoguan(Grant No. SHAOKE [2016]44/15).

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Copyright information

© Istituto di Informatica e Telematica del Consiglio Nazionale delle Ricerche 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsShaoguan UniversityShaoguanPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of MacauMacauPeople’s Republic of China

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