Comp. Appl. Math. https://doi.org/10.1007/s40314-018-0660-0 Discovery of new complementarity functions for NCP and SOCCP 1 2 Peng-Fei Ma · Jein-Shan Chen · 2 3 Chien-Hao Huang · 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
Computational and Applied Mathematics – Springer Journals
Published: Jun 6, 2018
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