Comp. Appl. Math.
Discovery of new complementarity functions for NCP
· Jein-Shan Chen
· Chun-Hsu Ko
Received: 25 February 2017 / Revised: 20 May 2018 / Accepted: 30 May 2018
© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018
Abstract It is well known that complementarity functions play an important role in dealing
with complementarity problems. In this paper, we propose a few new classes of com-
plementarity functions for nonlinear complementarity problems and second-order cone
complementarity problems. The constructions of such new complementarity functions are
based on discrete generalization which is a novel idea in contrast to the continuous general-
ization of Fischer–Burmeister function. Surprisingly, these new families of complementarity
functions possess continuous differentiability even though they are discrete-oriented exten-
sions. This feature enables that some methods like derivative-free algorithm can be employed
directly for solving nonlinear complementarity problems and second-order cone comple-
mentarity problems. This is a new discovery to the literature and we believe that such new
complementarity functions can also be used in many other contexts.
Communicated by Jinyun Yuan.
Peng-Fei Ma This research was supported by a grant from the National Natural Science Foundation of
Jein-Shan Chen The author’s work is supported by Ministry of Science and Technology, Taiwan.
Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou,
Zhejiang 310023, P.R. China
Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan
Department of Electrical Engineering, I-Shou University, Kaohsiung 840, Taiwan