Monotone and Accretive Vector Fields on Riemannian Manifolds |
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| Authors: | J H Wang G López V Martín-Márquez C Li |
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| Institution: | (1) Department of Mathematics, Royal Military College of Canada, Kingston ON K7K 7B4, STN Forces, Canada;(2) School of Mathematics, The University of Birmingham, The Watson Building Edgbaston, Birmingham, B15 2TT |
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| 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 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. |
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