Newton-type Method For A Class Of Nonsmooth Parametric Generalized Equations In Banach Space

Parametric generalized equation has broad applications in nonsmooth optimization,and classical Newton-type algorithms play an important role in solving generalized equations.In this thesis,we introduce the concept of second-order parametric point-based approximation and construct a generalized Newton-type algorithm for nonsmooth generalized equations.Under the assumption of metric regularity,we study feasibility of the algorithm and obtain quadratic convergence rate.At the same time,we study Lipschitz-like continuity of the infinite sequence generated by the algorithm with respect to disturbance variable.For nonparametric generalized equations,we introduce a restricted Newton-type algorithm,provide two convergence conditions,and conclude that any sequence generated by this algorithm converges at least linearly to the solution of the generalized equation.