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Numerical Algorithms

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22-08-2023 | Original Paper

The nonsmooth Newton’s method for the horizontal nonlinear complementarity problem

Authors: Xin-Hui Shao, Zhe Wang

Published in: Numerical Algorithms | Issue 1/2024

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Abstract

In this paper, we establish a modulus-based nonsmooth Newton’s method for solving a class of horizontal nonlinear complementarity problems and prove the nearly quadratic convergence of the method under certain assumptions. Based on the analysis of convergence, we give the selection strategy for the approximate iteration vector and propose the improved modulus-based nonsmooth Newton’s method. Finally, numerical experiments show that the new methods are superior to the modulus-based matrix iterative method regarding computational efficiency.

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Title: The nonsmooth Newton’s method for the horizontal nonlinear complementarity problem
Authors: Xin-Hui Shao
Zhe Wang
Publication date: 22-08-2023
Publisher: Springer US
Published in: Numerical Algorithms / Issue 1/2024
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-023-01640-8

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