A Newton iteration for differentiable set-valued maps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:399

Article

Gaydu, Michael¹  Geoffroy, Michel H.¹ 

[1] Univ Antilles Guyane, LAMIA, Dept Math, Pointe a Pitre, Guadeloupe, France

关键词: Variational inclusions;    Successive approximations;    H-differentiability;    Positively homogeneous mappings;   

DOI  :  10.1016/j.jmaa.2012.10.012

来源: Elsevier

【 摘 要 】

We employ recent developments of generalized differentiation concepts for set-valued mappings and present a Newton-like iteration for solving generalized equations of the form f(x) F(x) there exists 0 where f is a single-valued function while F stands for a set-valued map, both of them being smooth mappings acting between two general Banach spaces X and Y. The Newton iteration we propose is constructed on the basis of a linearization of both f and F; we prove that, under suitable assumptions on the derivatives of f and F, it converges Q-linearly to a solution to the generalized equation in question. When we strengthen our assumptions, we obtain the Q-quadratic convergence of the method. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free