What is the generalization of natural residual function for NCP
It is well known that the generalized Fischer Burmeister is a natural extension of the popular Fischer Burmeister function NCP function, in which the 2 norm is replaced by general p norm. As for another popular natural residual NCP function, its generalization was unknown during the past three decades. In this short communication, we answer this long standing open question. In particular, we propose the generalization of natural residual function for NCP, which possesses twice differentiability. This feature enables that many methods like Newton method can be employed directly for solving NCP. This is a new discovery to the literature and we believe that such generalized function can also be employed in many other contexts. Corresponding author. The author's work is supported by Ministry of Science and Technology, Taiwan. E mail: chko@isu.edu.tw E mail: cantor0968@gmail.com