Semismooth Newton Algorithm For NCP With A Non-Monotone Line Search

The research of the semi-smooth Newton algorithm began in the early 1990s. It rapidly developed with the further study on semi-smooth problems and became one of the extremely active methods in the optimization field. The monotonous line search was taken in the past semi-smooth algorithm. However, in practical problems, non-monotone line search can improve the numerical results and possibilities of finding the numerical optimization solution. Non-monotone line search can bypass some minimal points and get better solutions and it has been highly effective for some bad function in the optimization.In this paper, we propose a new semi-smooth Newton algorithm with non- monotone line search for complementarlity problems and analyze its convergence behavior. It is globally convergent and locally super-linearly convergent under some assumptions. We do some numerical implementations for this algorithm.