Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Riemannian manifold
  • generalized equation
  • Newton's method
  • metric regularity
  • variational inclusion

Suggested citation

S. Adly, H. V. Ngai, N. V. Vu. “Newton-Type Method for Solving Generalized Equations on Riemannian Manifolds.” Journal of Convex Analysis 25 (2018), No. 2, 341–370.

Copyright Heldermann Verlag 2018