Newton's method for solving generalized equations: Kantorovich's and Smale's approaches
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Van Vu Nguyen(Université de Limoges)
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Europe/Paris
XLIM Salle X.203
XLIM Salle X.203
FST-Université de Limoges,
123, Av. Albert Thomas.
Description
In this talk, we will discuss about the Newton-type iteration for solving generalized equation involving the set-valued mapping. We extend the classical Kantorovich's and alpha-Smale's theorems which ensure the existence as well as the convergence of such a Newton's sequence into the case of inclusion $0 \in f(x) + F(x)$. The quadratic convergence are also established under suitable assumptions. Our approach is based on tools from variational analysis, where the metric regularity concept plays an important role in our analysis.