TY - JOUR
T1 - Metrically Regular Mapping and Its Utilization to Convergence Analysis of a Restricted Inexact Newton-Type Method
AU - Harunor Rashid , Mohammed
JO - Journal of Computational Mathematics
VL - 1
SP - 44
EP - 69
PY - 2021
DA - 2021/11
SN - 40
DO - http://doi.org/10.4208/jcm.2005-m2019-0019
UR - https://global-sci.org/intro/article_detail/jcm/19969.html
KW - Generalized equation, Restricted inexact Newton-type method, Metrically regular mapping, Partial Lipschitz-like mapping, Semilocal convergence.
AB - <p style="text-align: justify;">In the present paper, we study the restricted inexact Newton-type method for solving the generalized equation $0\in f(x)+F(x)$, where $X$ and $Y$ are Banach spaces, $f:X\to Y$ is a Fréchet differentiable function and $F\colon X\rightrightarrows Y$ is a set-valued mapping with closed graph. We establish the convergence criteria of the restricted inexact Newton-type method, which guarantees the existence of any sequence generated by this method and show this generated sequence is convergent linearly and quadratically according to the particular assumptions on the Fréchet derivative of $f$. Indeed, we obtain semilocal and local convergence results of restricted inexact Newton-type method for solving the above generalized equation when the Fréchet derivative of $f$ is continuous and Lipschitz continuous as well as $f+F$ is metrically regular. An application of this method to variational inequality is given. In addition, a numerical experiment is given which illustrates the theoretical result.</p>