Monotone and Accretive Vector Fields on Riemannian Manifolds
By Jinhua Wang, Genaro López, Victoria Martín-Márquez, Chong Li, Chong Li. 2010
126 citations recorded by the source corpus.
The relationship between monotonicity and accretivity on Riemannian manifolds is studied in this paper and both concepts are proved to be equivalent in Hadamard manifolds. As a consequence an iterative method is obtained for approximating singularities of Lipschitz continuous, strongly monotone mappings. We also establish the equivalence between the strong convexity of functions and the strong monotonicity of its subdifferentials on Riemannian manifolds. These results are then applied to solve the minimization of convex functions on Riemannian manifolds.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/60d7414be0fd4fdec3e7daa903dd14e61aec3f18
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Proximal point method for a special class of nonconvex functions on Hadamard manifolds (2008, unknown): “The extension of the concepts and techniques of the Mathematical Programming from Euclidean space to Riemannian manifolds occurs naturally and has been frequently done in recent years, with a theoretical purpose as well as to obtain effective algorithms; see Absil et all [1], Attouch et all [2], Aza”
- Resolvents of Set-Valued Monotone Vector Fields in Hadamard Manifolds (2011, background): “Then B is strongly monotone by inequality (9); see also [10] and [48].”