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Generalized AOR Method for Solving Absolute Complementarity Problems

Author

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  • Muhammad Aslam Noor
  • Javed Iqbal
  • Khalida Inayat Noor
  • E. Al-Said

Abstract

We introduce and consider a new class of complementarity problems, which is called the absolute value complementarity problem. We establish the equivalence between the absolute complementarity problems and the fixed point problem using the projection operator. This alternative equivalent formulation is used to discuss the existence of a solution of the absolute value complementarity problem. A generalized AOR method is suggested and analyzed for solving the absolute the complementarity problems. We discuss the convergence of generalized AOR method for the L -matrix. Several examples are given to illustrate the implementation and efficiency of the method. Results are very encouraging and may stimulate further research in this direction.

Suggested Citation

  • Muhammad Aslam Noor & Javed Iqbal & Khalida Inayat Noor & E. Al-Said, 2012. "Generalized AOR Method for Solving Absolute Complementarity Problems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, April.
    • Handle: RePEc:hin:jnljam:743861
    DOI: 10.1155/2012/743861
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    Cited by:

    1. Yuan Liang & Chaoqian Li, 2023. "Modified Picard-like Method for Solving Absolute Value Equations," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    2. Yuan Li & Hai-Shan Han & Dan-Dan Yang, 2014. "A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems," Journal of Mathematics, Hindawi, vol. 2014, pages 1-10, September.

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