Geodesic
Newton-Type Method for Solving Generalized Equations on Riemannian Manifolds
Journal of convex analysis, Tome 25 (2018) no. 2, pp. 341-37
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This paper is devoted to the study of Newton-type algorithm for solving inclusions involving set-valued maps defined on Riemannian manifolds. We provide some sufficient conditions ensuring the existence as well as the quadratic convergence of Newton sequence. The material studied in this paper is based on Riemannian geometry as well as variational analysis, where metric regularity property is a key point.
Mots-clés : Riemannian manifold, generalized equation, Newton's method, metric regularity, variational inclusion 
@article{JCA_2018_25_2_JCA_2018_25_2_a1,
     author = {S. Adly and H. V. Ngai and N. V. Vu},
     title = {Newton-Type {Method} for {Solving} {Generalized} {Equations} on {Riemannian} {Manifolds}},
     journal = {Journal of convex analysis},
     pages = {341--37},
     year = {2018},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a1/}
}
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S. Adly; H. V. Ngai; N. V. Vu. Newton-Type Method for Solving Generalized Equations on Riemannian Manifolds. Journal of convex analysis, Tome 25 (2018) no. 2, pp. 341-37. http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a1/