Newton Algorithm And Its Convergence Analysis Of A Generalized Equation

In this paper, we consider the generalized equation f(p,x)+Q(x) (?)0 and study the implicit function theorem for generalized equation is given under the assumption of strong metric regularity of set-valued mapping Q. Further, the rate of convergence of Newton algorithm is discussed, consider a solution (p, x), and x ∈ S(p) (S(p)=(p| f(p,x)+Q(x) (?)0} is a solution mapping). Assume f is contin-uously Frechet differentiable in x with dervative denoted by Dxf(p,x), we studies the Newton iterative procedure f(p, xk)+Dxf(p, xk)(xk+1-xk)+Q(xk+)) (?)0 show that this method is second order convergence, if the mapping Q is strongly metrically regular at x for 0 and f is Lipschitz continuous with respect to both vari-ables in a neighborhood of the point (p, x).