# 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

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. ### Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

### Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial