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New NCP-Functions and Their Properties

Author

Listed:
  • C. Kanzow

    (University of Hamburg)

  • N. Yamashita

    (Kyoto University)

  • M. Fukushima

    (Kyoto University)

Abstract

Recently, Luo and Tseng proposed a class of merit functions for the nonlinear complementarity problem (NCP) and showed that it enjoys several interesting properties under some assumptions. In this paper, adopting a similar idea to that of Luo and Tseng, we present new merit functions for the NCP, which can be decomposed into component functions. We show that these merit functions not only share many properties with the one proposed by Luo and Tseng but also enjoy additional favorable properties owing to their decomposable structure. In particular, we present fairly mild conditions under which these merit functions have bounded level sets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:1:d:10.1023_a:1022659603268
    DOI: 10.1023/A:1022659603268
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    References listed on IDEAS

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    1. Jong-Shi Pang, 1987. "A Posteriori Error Bounds for the Linearly-Constrained Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 474-484, August.
    2. 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.
    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.
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    Cited by:

    1. Azam Asanjarani, 2023. "A Finsler Geometrical Programming Approach to the Nonlinear Complementarity Problem of Traffic Equilibrium," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 797-809, March.
    2. 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.
    3. Xiaojun Chen & Masao Fukushima, 2005. "Expected Residual Minimization Method for Stochastic Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1022-1038, November.
    4. J.-S. Chen & Z.-H. Huang & C.-Y. She, 2011. "A new class of penalized NCP-functions and its properties," Computational Optimization and Applications, Springer, vol. 50(1), pages 49-73, September.
    5. Aurél Galántai, 2012. "Properties and construction of NCP functions," Computational Optimization and Applications, Springer, vol. 52(3), pages 805-824, July.
    6. S. H. Pan & J.-S. Chen, 2009. "Growth Behavior of Two Classes of Merit Functions for Symmetric Cone Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 167-191, April.
    7. Boshi Tian & Yaohua Hu & Xiaoqi Yang, 2015. "A box-constrained differentiable penalty method for nonlinear complementarity problems," Journal of Global Optimization, Springer, vol. 62(4), pages 729-747, August.
    8. J. M. Peng, 1998. "Derivative-Free Methods for Monotone Variational Inequality and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 235-252, October.
    9. N. Yamashita, 1998. "Properties of Restricted NCP Functions for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 701-717, September.
    10. Samir Adly & Hadia Rammal, 2013. "A new method for solving Pareto eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 55(3), pages 703-731, July.
    11. S. Mohsen Miri & Sohrab Effati, 2015. "On Generalized Convexity of Nonlinear Complementarity Functions," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 723-730, February.
    12. Gaoxi Li & Xinmin Yang, 2021. "Convexification Method for Bilevel Programs with a Nonconvex Follower’s Problem," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 724-743, March.
    13. Patrick Mehlitz, 2020. "A comparison of solution approaches for the numerical treatment of or-constrained optimization problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 233-275, May.

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