Publications in Scientific Journals:
R. Cibulka, A. Dontchev, J. Preininger, T. Roubal, V.M. Veliov:
"Kantorovich-Type Theorems for Generalized Equations";
Journal of Convex Analysis,
25
(2018),
2;
459
- 486.
English abstract:
We study convergence of the Newton method for solving generalized equations of the form $f(x)+F(x)\ni 0,$ where $f$ is a continuous but not necessarily smooth function and $F$ 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.
Keywords:
Newton's method, generalized equation, variational inequality, metric regularity, Kantorovich theorem, linear/superlinear/quadratic convergence.
Electronic version of the publication:
https://publik.tuwien.ac.at/files/publik_258570.pdf
Created from the Publication Database of the Vienna University of Technology.