Newton’s method for variational inequality problems: Smale’s point estimate theory under the γ-condition

Abstract

In the present paper, we study Newton’s method for variational inequality problems. Under the -condition, the generalized -theory and -theory for Newton’s method are established. As an application, Smale’s point estimate theory for analytic mappings are given.

Keywords:

• variational inequality problems
• Newton’s method
• the γ-condition
• Smale’s point estimate theory

AMS Subject Classifications:

• 49J40
• 65J05

Funding

The research of the first author is partially supported by an NSF [grant DMS-1203845] and Hong Kong RGC competitive earmarked research [grant 601410]. The research of the second author was partially supported by the National Natural Science Foundation of China [grant 11001241, 11371325] and by Zhejiang Provincial Natural Science Foundation of China [grant LY13A010011]. The research of the third author was partially supported by a grant from NSC of Taiwan [NSC 102-2221-E-037-004-MY3].

Notes

Dedicated to Professor Boris S. Mordukhovich on the occasion of his 65th Birthday.