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A Two‐Parametric Class of Merit Functions for the Second‐Order Cone Complementarity Problem

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  • Xiaoni Chi
  • Zhongping Wan
  • Zijun Hao

Abstract

We propose a two‐parametric class of merit functions for the second‐order cone complementarity problem (SOCCP) based on the one‐parametric class of complementarity functions. By the new class of merit functions, the SOCCP can be reformulated as an unconstrained minimization problem. The new class of merit functions is shown to possess some favorable properties. In particular, it provides a global error bound if F and G have the joint uniform Cartesian P‐property. And it has bounded level sets under a weaker condition than the most available conditions. Some preliminary numerical results for solving the SOCCPs show the effectiveness of the merit function method via the new class of merit functions.

Suggested Citation

  • Xiaoni Chi & Zhongping Wan & Zijun Hao, 2013. "A Two‐Parametric Class of Merit Functions for the Second‐Order Cone Complementarity Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:571927
    DOI: 10.1155/2013/571927
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    References listed on IDEAS

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    1. Jein-Shan Chen, 2006. "Two classes of merit functions for the second-order cone complementarity problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 495-519, December.
    2. Lingchen Kong & Levent Tunçel & Naihua Xiu, 2009. "Vector-Valued Implicit Lagrangian For Symmetric Cone Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(02), pages 199-233.
    3. 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.
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