PROPERTIES OF A CLASS OF NCP-FUNCTIONS AND A RELATED SEMISMOOTH NEWTON METHOD FOR COMPLEMENTARITY PROBLEMS

摘要

In this paper, we aim to explore properties of a class of NCP-functions and investigate a related semismooth Newton method for complementarity problems. Some favorite properties about the class of NCP-functions and its merit function are discussed including strong semismoothness, continuous differentiability and the nonsingularity of the element in C-subdifferential. In particular, we present an exact expression of the generalized gradient for the NCP-function. The level boundedness of the merit function is discussed. Based on these results, we investigate a semismooth Newton method and give its convergence analysis. As an application, we use this method to solve the frictionless contact problem.