Journal of Optimization Theory and Applications

, Volume 146, Issue 3, pp 691–708 | Cite as

Monotone and Accretive Vector Fields on Riemannian Manifolds

  • J. H. Wang
  • G. López
  • V. Martín-Márquez
  • C. Li


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.


Hadamard manifold Monotone vector field Accretive vector field Singularity Fixed point Iterative algorithm Convex function 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • J. H. Wang
    • 1
  • G. López
    • 2
  • V. Martín-Márquez
    • 2
  • C. Li
    • 3
    • 4
  1. 1.Department of Applied MathematicsZhejiang University of TechnologyHangzhouP.R. China
  2. 2.Departamento de Análisis MatemáticoUniversidad de SevillaSevillaSpain
  3. 3.Department of MathematicsZhejiang UniversityHangzhouP.R. China
  4. 4.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia

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