METRICALLY REGULAR MAPPING AND ITS UTILIZATION TO CONVERGENCE ANALYSIS OF A RESTRICTED INEXACT NEWTON-TYPE METHOD  

作　　者：Mohammed Harunor Rashid 

机构地区：[1]Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]Department of Mathematics,Faculty of Science,University of Rajshahi,Rajshahi-6205,Bangladesh

出　　处：《Journal of Computational Mathematics》2022年第1期44-69,共26页计算数学（英文）

基　　金：supported by CAS-President International Fellowship Initiative(PIFI)from the Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,China.

摘　　要：In the present paper,we study the restricted inexact Newton-type method for solving the generalized equation 0∈f(x)+F(x),where X and Y are Banach spaces,f:X→Y is a Frechet differentiable function and F:X■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 Frechet 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 Frechet 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.

关 键 词：Generalized equation Restricted inexact Newton-type method Metrically regular mapping Partial Lipschitz-like mapping Semilocal convergence. 

分 类 号：O175[理学—数学]