Cibulka, R., Dontchev, A. L., Preininger, J., Veliov, V. M., & Roubal, T. (2018). Kantorovich-Type Theorems for Generalized Equations. Journal of Convex Analysis, 25(2), 459–486. http://hdl.handle.net/20.500.12708/144705
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.
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Research Areas:
Mathematical Methods in Economics: 20% Modelling and Simulation: 80%