Geodesic
Kantorovich-Type Theorems for Generalized Equations
Journal of convex analysis, Tome 25 (2018) no. 2, pp. 459-486
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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.
Classification : 49J53, 49J40, 65J15, 90C30
Mots-clés : Newton's method, generalized equation, variational inequality, metric regularity, Kantorovich theorem, linear/superlinear/quadratic convergence 
@article{JCA_2018_25_2_JCA_2018_25_2_a7,
     author = {R. Cibulka and A. L. Dontchev and J. Preininger and T. Roubal and V. Veliov},
     title = {Kantorovich-Type {Theorems} for {Generalized} {Equations}},
     journal = {Journal of convex analysis},
     pages = {459--486},
     year = {2018},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a7/}
}
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%J Journal of convex analysis
%D 2018
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R. Cibulka; A. L. Dontchev; J. Preininger; T. Roubal; V. Veliov. Kantorovich-Type Theorems for Generalized Equations. Journal of convex analysis, Tome 25 (2018) no. 2, pp. 459-486. http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a7/