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A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems

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  • Yuan Li
  • Hai-Shan Han
  • Dan-Dan Yang

Abstract

We consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton method is proposed for solving the absolute value linear complementary problem. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems is positive definite and its singular values exceed 1. Numerical results show that our proposed method is very effective and efficient.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jjmath:560578
    DOI: 10.1155/2014/560578
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    References listed on IDEAS

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    1. 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.
    2. Muhammad Aslam Noor & Javed Iqbal & Eisa Al-Said, 2012. "Residual Iterative Method for Solving Absolute Value Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, March.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    4. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    5. S. Wang & X. Q. Yang & K. L. Teo, 2006. "Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 227-254, May.
    6. C. Zhang & Q. J. Wei, 2009. "Global and Finite Convergence of a Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 391-403, November.
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