Newton-type method for solving generalized equations on Riemannian manifolds

Samir Adly (1) , Huynh Van Ngai (2) , Nguyen Van Vu (2)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information
2 Quy Nhon University

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

Domaines: Optimisation et contrôle [math.OC]

Samir Adly, Huynh Van Ngai, Nguyen Van Vu. Newton-type method for solving generalized equations on Riemannian manifolds. Journal of Convex Analysis, 2018, 25 (2), pp.341-370. ⟨hal-02386018⟩