On NCP-Functions

. In this paper we reformulate several NCP-functions for the nonlinear complementarity problem (NCP) from their merit function forms and study some important properties of these NCP-functions. We point out that some of these NCP-functions have all the nice properties investigated by Chen, Chen and Kanzow [2] for a modified Fischer-Burmeister function, while some other NCP-functions may lose one or several of these properties. We also provide a modified normal map and a smoothing technique to overcome the limitation of these NCP-functions. A numerical comparison for the behaviour of various NCP-functions is provided. Keywords: nonlinear complementarity problem, NCP-function, normal map, smoothing A tribute to Olvi from Liqun Qi Olvi was one of my teachers at University of Wisconsin-Madison during my Ph.D. study. He had always encouraged me to work on optimization theory and algorithms, on solution of optimization problems, instead of abstract analysis. Olvi is always helpful and frien..