Extended Newton-type Method for Nonsmooth Generalized Equation under n , α -point-based Approximation.

Let X and Y be Banach spaces and omega & SUBE;X. Let f:omega?Y be a single valued function which is nonsmooth. Suppose that F:X?2(Y) is a set-valued mapping which has closed graph. In the present paper, we study the extended Newton-type method for solving the nonsmooth generalized equation 0 is an element of f(x)+F(x) and analyze its semilocal and local convergence under the conditions that f+F-1 is Lipschitz-like and f admits a certain type of approximation which generalizes the concept of point-based approximation so-called (n,alpha)-point-based approximation. Applications of (n,alpha)-point-based approximation are provided for smooth functions in the cases n=1 and n=2 as well as for normal maps. In particular, when 0 更多