Two Confined Newton-type Methods For Nonsmooth Generalized Equations And Their Convergence Analysis

Generalized equation 0?f(x)+F(x) can be considered as a uniform framework for many optimization problems,variational problems and equilibrium problems.In recent years,various Newton-type methods for solving generalized equations as well as their convergence analysis have received extensive attention from many researchers.This thesis mainly contains two parts.In the first part,under the assumption that the single-valued function 1)has weak point-based approximation of order 9)+ -1,we study higher order convergence of a Newton-type method as well as a confined Newton-type method.The second part assumes that the set-valued mapping has strict prederivative.Based on this,a class of confined Newton-type algorithm is proposed and its semi-local convergence is studied.