International audienceResults on stability of both local and global metric regularity under set-valued perturbations are presented. As an application, we study (super)linear convergence of a Newton- type iterative process for solving generalized equations. We investigate several iterative schemes such as the inexact Newton’s method, the nonsmooth Newton’s method for semismooth functions, the inexact proximal point algorithm, etc. Moreover, we also cover a forward-backward splitting algorithm for finding a zero of the sum of two multivalued (not necessarily monotone) operators. Finally, a globalization of the Newton’s method is discussed

5This paper studies stability of error bounds for convex constraint systems 6 in Banach spaces. We show that certain known sufficient conditions for local 7 and global error bounds actually ensure error bounds for the family of func-8 tions being in a sense small perturbations of the given one. A single inequality 9 as well as semi-infinite constraint systems are considered.

No abstract

No abstract

International audienceIn this paper, we study Newton-type methods for solving generalized equations involving set-valued maps in Banach spaces. Kantorovich-type theorems (both local and global versions) are proved as well as the quadratic convergence of the Newton sequence. We also extend Smale's classical (α,γ)-theory to generalized equations. These results are new and can be considered as an extension of many known ones in the literature for classical nonlinear equations. Our approach is based on tools from variational analysis. The metric regularity concept plays an important role in our analysis