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Monotone and Accretive Vector Fields on Riemannian Manifolds

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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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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang, 310032, P.R. China

    J. H. Wang

  2. Departamento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080, Sevilla, Spain

    G. López & V. Martín-Márquez

  3. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

    C. Li

  4. Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    C. Li

Authors
  1. J. H. Wang
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  2. G. López
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  3. V. Martín-Márquez
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  4. C. Li
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Corresponding author

Correspondence to J. H. Wang.

Additional information

Communicated by J.-C. Yao.

G. López partially supported by Ministerio de Ciencia e Innovación, Grant MTM2009-110696-C02-01 and Junta de Andalucía, Grant FQM-127.

V. Martín-Márquez partially supported by Ministerio de Ciencia e Innovación, Grants MTM2009-110696-C02-01 and AP2005-1018, and Junta de Andalucía, Grant FQM-127.

C. Li partially supported by Ministerio de Ciencia e Innovación, Grant MTM2009-110696-C02-01, Spain; the National Natural Science Foundations of China (Grant No. 10731060).

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Wang, J.H., López, G., Martín-Márquez, V. et al. Monotone and Accretive Vector Fields on Riemannian Manifolds. J Optim Theory Appl 146, 691–708 (2010). https://doi.org/10.1007/s10957-010-9688-z

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  • DOI: https://doi.org/10.1007/s10957-010-9688-z

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