On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem

It has been an open question that whether the family of merit functions ψp (p > 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 ψp is smooth for The author’s work is supported by National Young Natural Science Foundation (No. 10901058) and Guangdong Natural Science Foundation (No. 9251802902000001). E-mail: [email protected]. The authors’ work is supported by Basic Science Research Program through NRF Grant No. 20120001740. E-mail: [email protected]. The author’s work is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MEST) (No.2012-005191). E-mail: [email protected]. Corresponding author. Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author’s work is supported by National Science Council of Taiwan. E-mail: [email protected].