Journal of Convex Analysis 25 (2018), No. 2, 341--370
Copyright Heldermann Verlag 2018
Newton-Type Method for Solving Generalized Equations on Riemannian Manifolds
Samir Adly
Laboratoire Xlim, Université de Limoges, 123 Avenue Albert Thomas, 87060 Limoges, France
samir.adly@unilim.fr
Huynh Van Ngai
Dept. of Mathematics, University of Quy Nhon, 170 An Duong Vuong, Quy Nhon, Vietnam
ngaivn@yahoo.com
Nguyen Van Vu
Laboratoire Xlim, Université de Limoges, 123 Avenue Albert Thomas, 87060 Limoges, France
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.
Keywords: Riemannian manifold, generalized equation, Newton's method, metric regularity, variational inclusion.
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