DOI: 10.68381/jca25031 ISSN: 0944-6532
Kantorovich-Type Theorems for Generalized Equations
Radek Cibulka, Asen L. Dontchev, Jakob Preininger, Tomáš Roubal, Vladimir Veliov
We study convergence of the Newton method for solving generalized equations of the form
f(x)+F(x)\ni 0,
f
(
x
)
+
F
(
x
)
∋
0
,
where
f
f
is a continuous but not necessarily smooth function and
F
F
is a set-valued mapping with closed graph, both acting in Banach spaces. We present a Kantorovich-type theorem concerning r-linear convergence for a general algorithmic strategy covering both nonsmooth and smooth cases. Under various conditions we obtain higher-order convergence. Examples and computational experiments illustrate the theoretical results.