
Journal of Convex Analysis 25 (2018), No. 2, 459486 Copyright Heldermann Verlag 2018 KantorovichType Theorems for Generalized Equations Radek Cibulka NTIS  Dept. of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 22, 306 14 Pilsen, Czech Republic cibi@kma.zcu.cz Asen L. Dontchev Mathematical Reviews, 416 Fourth Street, Ann Arbor, MI 481078604, U.S.A. ald@ams.org Jakob Preininger Institute of Statistics and Mathematical Methods in Economics, University of Technology, Wiedner Hauptstrasse 8, 1040 Vienna, Austria jakob.preininger@tuwien.ac.at Tomás Roubal NTIS  Dept. of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 22, 306 14 Pilsen, Czech Republic roubalt@students.zcu.cz Vladimir Veliov Institute of Statistics and Mathematical Methods in Economics, University of Technology, Wiedner Hauptstrasse 8, 1040 Vienna, Austria veliov@tuwien.ac.at [Abstractpdf] 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 setvalued mapping with closed graph, both acting in Banach spaces. We present a Kantorovichtype theorem concerning rlinear convergence for a general algorithmic strategy covering both nonsmooth and smooth cases. Under various conditions we obtain higherorder 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. MSC: 49J53, 49J40, 65J15, 90C30 [ Fulltextpdf (191 KB)] for subscribers only. 