Abstract
In this paper we study the nonlinear weighted complementarity problem (denoted by NWCP). We first introduce a smoothing function which can be used to reformulate the NWCP as a system of smooth nonlinear equations. Then we propose a new smoothing-type algorithm to solve the NWCP which adopts a nonmonotone line search scheme. In each iteration, our algorithm solves one linear system of equations and performs one line search. Under suitable assumptions, we prove that the proposed algorithm is globally and locally quadratically convergent. Some numerical results are reported.
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Acknowledgements
The authors are grateful to the referees for their valuable suggestions that improved the paper greatly. This work was supported by Nanhu Scholars Program for Young Scholars of Xinyang Normal University.
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Liu, Z., Tang, J. A new smoothing-type algorithm for nonlinear weighted complementarity problem. J. Appl. Math. Comput. 64, 215–226 (2020). https://doi.org/10.1007/s12190-020-01352-5
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DOI: https://doi.org/10.1007/s12190-020-01352-5
Keywords
- Nonlinear weighted complementarity problem
- Smoothing Newton algorithm
- Nonmonotone line search
- Quadratical convergence