Local convergence analysis of Newton's method for solving strongly regular generalized equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:458

Article

Ferreira, O. P.¹  Silva, G. N.² 

[1] Univ Fed Goias, IME, CP-131, BR-74001970 Goiania, Go, Brazil

[2] UFOB, CCET, BR-47808021 Barreiras, BA, Brazil

关键词: Generalized equation;    Newton's method;    Strong regularity;    Majorant condition;   

DOI  :  10.1016/j.jmaa.2017.09.023

来源: Elsevier

【 摘 要 】

In this paper, we consider Newton's method for solving a generalized equation of the form f(x)+F(x) is an element of 0, where f : Omega -> Y is continuously differentiable, X and Y are Banach spaces, Omega subset of X is open, and F : X paired right arrows Y has a nonempty closed graph. We show that, under strong regularity of the equation, the method is locally convergent to a solution with superlinear/quadratic rate. Our analysis, which is based on general majorant condition, enables us to obtain a convergence result under the Lipschitz, Smale's, and Nesterov-Nemirovskii's self-concordant conditions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free