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Monotone and accretive vector fields on Riemannian manifolds

 

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Opened Access Monotone and accretive vector fields on Riemannian manifolds
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Author: Wang, Jinhua
López Acedo, Genaro
Martín Márquez, Victoria
Li, Chong
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2010-09
Published in: Journal of Optimization Theory and Applications, 146 (3), 691-708.
Document type: Article
Abstract: 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 convex functions and the strong monotonicity of its subdifferentials on Riemannian manifolds. These results are then applied to solve the minimization problem of convex functions on Riemannian manifolds.
Cite: Wang, J., López Acedo, G., Martín Márquez, V. y Li, C. (2010). Monotone and accretive vector fields on Riemannian manifolds. Journal of Optimization Theory and Applications, 146 (3), 691-708.
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URI: http://hdl.handle.net/11441/48265

DOI: 10.1007/s10957-010-9688-z

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