## Journal of Applied Mathematics

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

#### 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.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 571927, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808023

Digital Object Identifier
doi:10.1155/2013/571927

Mathematical Reviews number (MathSciNet)
MR3066640

Zentralblatt MATH identifier
1278.90401

#### Citation

Chi, Xiaoni; Wan, Zhongping; Hao, Zijun. A Two-Parametric Class of Merit Functions for the Second-Order Cone Complementarity Problem. J. Appl. Math. 2013 (2013), Article ID 571927, 10 pages. doi:10.1155/2013/571927. https://projecteuclid.org/euclid.jam/1394808023

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