# MathSciDoc: An Archive for Mathematician ∫

#### Optimization and Controlmathscidoc:1910.43901

Mathematics of Computation, 83, (287), 1143-1171, 2014
It has been an open question whether the family of merit functions $\psi _p\(p&gt; 1)$, the generalized Fischer-Burmeister (FB) merit function, associated to the second-order cone is smooth or not. In this paper we answer it partly, and show that \psi _p is smooth for \psi _p , and we provide the condition for its coerciveness. Numerical results are reported to illustrate the influence of \psi _p on the performance of the merit function method based on \psi _p .
@inproceedings{shaohua2014on,
title={On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem},
author={Shaohua Pan, Sangho Kum, Yongdo Lim, and Jein-Shan Chen},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224149480190430},
booktitle={Mathematics of Computation},
volume={83},
number={287},
pages={1143-1171},
year={2014},
}

Shaohua Pan, Sangho Kum, Yongdo Lim, and Jein-Shan Chen. On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem. 2014. Vol. 83. In Mathematics of Computation. pp.1143-1171. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224149480190430.