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

Author

Listed:
  • Hua Zheng

    (Shaoguan University)

  • Ling Liu

    (Shaoguan University)

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.

Suggested Citation

  • Hua Zheng & Ling Liu, 2019. "The Sign-Based Methods for Solving a Class of Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 480-499, February.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1361-y
    DOI: 10.1007/s10957-018-1361-y
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    References listed on IDEAS

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    1. Li-Li Zhang, 2014. "Two-Stage Multisplitting Iteration Methods Using Modulus-Based Matrix Splitting as Inner Iteration for Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 189-203, January.
    2. Wen, Baolian & Zheng, Hua & Li, Wen & Peng, Xiaofei, 2018. "The relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems of positive definite matrices," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 349-357.
    3. Xia, Zechen & Li, Chenliang, 2015. "Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 34-42.
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    Cited by:

    1. Yiyin Cao & Chuangyin Dang & Yabin Sun, 2022. "Complementarity Enhanced Nash’s Mappings and Differentiable Homotopy Methods to Select Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 533-563, February.

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