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


Authors: Shaohua Pan, Sangho Kum, Yongdo Lim and Jein-Shan Chen
Journal: Math. Comp. 83 (2014), 1143-1171
MSC (2010): Primary 90C33, 90C25
Published electronically: July 15, 2013
MathSciNet review: 3167453
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Abstract: It has been an open question whether the family of merit functions $ \psi _p\ (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 $ \psi _p$ is smooth for $ p\in (1,4)$, and we provide the condition for its coerciveness. Numerical results are reported to illustrate the influence of $ p$ on the performance of the merit function method based on $ \psi _p$.


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Additional Information

Shaohua Pan
Affiliation: School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, People’s Republic of China
Email: shhpan@scut.edu.cn

Sangho Kum
Affiliation: Department of Mathematics Education, Chungbuk National University, Cheongju 361-763, South Korea
Email: shkum@chungbuk.ac.kr

Yongdo Lim
Affiliation: Department of Mathematics, Sungkyunkwan University, Suwan 440-746, South Korea
Email: ylim@knu.ac.kr

Jein-Shan Chen
Affiliation: Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan
Email: jschen@math.ntnu.edu.tw

DOI: https://doi.org/10.1090/S0025-5718-2013-02742-1
Keywords: Second-order cones, complementarity problem, generalized FB merit function
Received by editor(s): August 15, 2010
Received by editor(s) in revised form: April 18, 2011, and August 7, 2012
Published electronically: July 15, 2013
Additional Notes: The first author’s work was supported by National Young Natural Science Foundation (No. 10901058) and the Fundamental Research Funds for the Central Universities (SCUT)
The second author’s work was supported by Basic Science Research Program through NRF Grant No. 2012-0001740.
The third author’s work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No.2012-005191).
Corresponding author: The fourth author is a member of the Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The fourth author’s work was supported by National Science Council of Taiwan.
Article copyright: © Copyright 2013 American Mathematical Society