R. Cibulka, A. Dontchev, J. Preininger, T. Roubal, V.M. Veliov:
"Kantorovich-Type Theorems for Generalized Equations";
Journal of Convex Analysis, 25 (2018), 2; S. 459 - 486.

Kurzfassung englisch:
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.

Newton's method, generalized equation, variational inequality, metric regularity, Kantorovich theorem, linear/superlinear/quadratic convergence.

Elektronische Version der Publikation:

Erstellt aus der Publikationsdatenbank der Technischen Universitšt Wien.