# Local convergence of Newton’s method for subanalytic variational inclusions

Local convergence of Newton’s method for subanalytic variational inclusions This paper concerns variational inclusions of the form $$0 \in f(x) + F(x)$$ where f is a single locally Lipschitz subanalytic function and F is a set-valued map acting in Banach spaces. We prove the existence and the convergence of a sequence (x k ) satisfying $$0 \in f(x_k)+\Delta f(x_k)(x_{k+1}-x_k)+F(x_{k+1})$$ where $$\Delta f(x_k)$$ lies to $$\partial f(x_k)$$ which is the Clarke Jacobian of f at the point x k . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Local convergence of Newton’s method for subanalytic variational inclusions

, Volume 12 (3) – Mar 12, 2008
9 pages

/lp/springer_journal/local-convergence-of-newton-s-method-for-subanalytic-variational-8urHxMmNmZ
Publisher
SP Birkhäuser Verlag Basel
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-007-2155-x
Publisher site
See Article on Publisher Site

### Abstract

This paper concerns variational inclusions of the form $$0 \in f(x) + F(x)$$ where f is a single locally Lipschitz subanalytic function and F is a set-valued map acting in Banach spaces. We prove the existence and the convergence of a sequence (x k ) satisfying $$0 \in f(x_k)+\Delta f(x_k)(x_{k+1}-x_k)+F(x_{k+1})$$ where $$\Delta f(x_k)$$ lies to $$\partial f(x_k)$$ which is the Clarke Jacobian of f at the point x k .

### Journal

PositivitySpringer Journals

Published: Mar 12, 2008

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