Newton’s method for solving inclusions using set-valued approximations

Abstract
Results on  stability of both local and global metric regularity under
set-valued perturbations are presented. As an application, we study
(super-)linear convergence of the Newton-type iterative process for
solving generalized equations.  The possibility to choose set-valued
approximations allows us to describe several iterative schemes in a
unified way (such as inexact Newton method, non-smooth Newton method for
semi-smooth functions, inexact proximal point algorithm, etc.). Moreover,
it also covers a forward-backward splitting algorithm for finding a common
zero of the sum of two multivalued (not necessarily  monotone) operators.
Finally, a globalization of the Newton’s method is discussed.
The theoretical results discussed in this talk may open a new field of
applications for the development of new algorithms for solving variational
problems using modern non-smooth analysis tools. This is a joint work with
R. Cibulka and H.V. Ngai

Posted on Oct 2, 2013 in Optimization and Equilibrium, Seminars