Journal of Applied Mathematics
Volume 2013 (2013), Article ID 571927, 10 pages
http://dx.doi.org/10.1155/2013/571927
Research Article

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

Xiaoni Chi,1,2 Zhongping Wan,1 and Zijun Hao1,3

1School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
2School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
3School of Information and Calculating Science, North University for Ethnics, Yinchuan 750021, China

Received 18 February 2013; Revised 16 May 2013; Accepted 20 May 2013

Academic Editor: Zhongxiao Jia

Copyright © 2013 Xiaoni Chi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 and have the joint uniform Cartesian -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.