Abstract
Let X and Y be Banach spaces. Let be a Fréchet differentiable function and be a set-valued mapping with closed graph. In this paper, a restricted Newton-type method has been introduced for solving the generalized equations of the form . Under some suitable conditions, we will establish the convergence criteria of the restricted Newton-type method, which ensures the existence and the convergence of any sequence generated by this method. More precisely, when the Fréchet derivative of f is continuous and Lipschitz continuous as well as is metrically regular, we analyze the semilocal and local convergence of the restricted Newton-type method. In addition, an example is given to show the reason for considering the metrically regular property instead of Lipschitz-like property of set-valued mapping in this paper.
Notes
No potential conflict of interest was reported by the authors.