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Some Properties Of A Class Of Merit Functions For Symmetric Cone Complementarity Problems

Author

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  • YONG-JIN LIU

    (Department of Mathematics, College of Science, Shantou University, Shantou 515063, P. R. China)

  • LI-WEI ZHANG

    (Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China)

  • YIN-HE WANG

    (Department of Mathematics, College of Science, Shantou University, Shantou 515063, P. R. China)

Abstract

In this paper, we extend a class of merit functions proposed by Kanzowet al.(1997) for linear/nonlinear complementarity problems to Symmetric Cone Complementarity Problems (SCCP). We show that these functions have several interesting properties, and establish a global error bound for the solution to the SCCP as well as the level boundedness of every merit function under some mild assumptions. Moreover, several functions are demonstrated to enjoy these properties.

Suggested Citation

  • Yong-Jin Liu & Li-Wei Zhang & Yin-He Wang, 2006. "Some Properties Of A Class Of Merit Functions For Symmetric Cone Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 473-495.
    • Handle: RePEc:wsi:apjorx:v:23:y:2006:i:04:n:s0217595906000991
    DOI: 10.1142/S0217595906000991
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    Citations

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    Cited by:

    1. Alberto Seeger & David Sossa, 2015. "Complementarity problems with respect to Loewnerian cones," Journal of Global Optimization, Springer, vol. 62(2), pages 299-318, June.
    2. J.-S. Chen, 2007. "Conditions for Error Bounds and Bounded Level Sets of Some Merit Functions for the Second-Order Cone Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 459-473, December.
    3. Nan Lu & Zheng-Hai Huang, 2014. "A Smoothing Newton Algorithm for a Class of Non-monotonic Symmetric Cone Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 446-464, May.
    4. 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.
    5. Cong Cheng & Lianjie Tang, 2023. "A Smoothing Method for Sparse Programs by Symmetric Cone Constrained Generalized Equations," Mathematics, MDPI, vol. 11(17), pages 1-19, August.
    6. S. H. Kum & Y. D. Lim, 2009. "Coercivity and Strong Semismoothness of the Penalized Fischer-Burmeister Function for the Symmetric Cone Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 377-383, August.

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