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The Sign-Based Methods for Solving a Class of Nonlinear Complementarity Problems

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Abstract

In this paper, using the sign patterns of the solution of the equivalent modulus equation, the resolution of the nonlinear complementarity problem shrinks to find the zero of a differentiable nonlinear function. Then, a sign-based Newton’s method is established by applying the Newton’s iteration. The theoretical analysis for the sign patterns of the solution of the equivalent modulus equation is given under the assumption of strictly complementarity. Moreover, by using the known modulus-based matrix splitting iteration method to detect the sign patterns of the solution of the equivalent modulus equation, a practical sign-detection Newton’s method is proposed. Numerical examples show that the new methods are efficient and accelerate the convergence performance with higher precision and less CPU time than the existing modulus-based matrix splitting iteration method and the projection-based matrix splitting iteration method, especially for the large sparse problems.

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Acknowledgements

The authors would like to thank the referees for their helpful comments. The work was supported by the National Natural Science Foundation of China (Grant No. 11601340) and the Science Foundation of Shaoguan University (Grant No. SY2016KJ15).

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  1. School of Mathematics and Statistics, Shaoguan University, Shaoguan, People’s Republic of China

    Hua Zheng & Ling Liu

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  1. Hua Zheng
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  2. Ling Liu
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Correspondence to Hua Zheng.

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Communicated by Suliman S. Al-Homidan.

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Zheng, H., Liu, L. The Sign-Based Methods for Solving a Class of Nonlinear Complementarity Problems. J Optim Theory Appl 180, 480–499 (2019). https://doi.org/10.1007/s10957-018-1361-y

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