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Error Bounds for R0-Type and Monotone Nonlinear Complementarity Problems

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  • B. Chen

Abstract

The paper generalizes the Mangasarian–Ren (Ref. 1) error bounds forlinear complementarity problems (LCPs) to nonlinear complementarity problems(NCPs). This is done by extending the concept of R 0-matrixto several R 0-type functions, which include a subset ofmonotone functions as a special case. Both local and global error bounds areobtained for R 0-type NCPs and some monotone NCPs.

Suggested Citation

  • B. Chen, 2001. "Error Bounds for R0-Type and Monotone Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 297-316, February.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:2:d:10.1023_a:1026434200384
    DOI: 10.1023/A:1026434200384
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    References listed on IDEAS

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    1. C. Kanzow & N. Yamashita & M. Fukushima, 1997. "New NCP-Functions and Their Properties," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 115-135, July.
    2. Francisco Facchinei, 1998. "Structural and Stability Properties of P 0 Nonlinear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 735-745, August.
    3. Z.-Q. Luo & O. L. Mangasarian & J. Ren & M. V. Solodov, 1994. "New Error Bounds for the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 880-892, November.
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    Cited by:

    1. Shuhuang Xiang & Xiaojun Chen, 2011. "Computation of generalized differentials in nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 50(2), pages 403-423, October.
    2. Zhang, Chao & Chen, Xiaojun & Sumalee, Agachai, 2011. "Robust Wardrop's user equilibrium assignment under stochastic demand and supply: Expected residual minimization approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 534-552, March.
    3. N. H. Xiu & J. Z. Zhang, 2002. "Global Projection-Type Error Bounds for General Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 213-228, January.
    4. C. Zhang & X. Chen, 2008. "Stochastic Nonlinear Complementarity Problem and Applications to Traffic Equilibrium under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 277-295, May.
    5. Yongchao Liu & Huifu Xu & Gui-Hua Lin, 2012. "Stability Analysis of One Stage Stochastic Mathematical Programs with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 537-555, February.
    6. Götz Alefeld & Zhengyu Wang, 2011. "Error Bounds for Nonlinear Complementarity Problems with Band Structure," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 33-51, July.

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    Keywords

    error bounds; R0-functions; complementarity problems;
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