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Journal of Optimization Theory and Applications

, Volume 159, Issue 1, pp 125–137 | Cite as

A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds

Article

Abstract

In this paper, a subgradient-type method for solving nonsmooth multiobjective optimization problems on Riemannian manifolds is proposed and analyzed. This method extends, to the multicriteria case, the classical subgradient method for real-valued minimization proposed by Ferreira and Oliveira (J. Optim. Theory Appl. 97:93–104, 1998). The sequence generated by the method converges to a Pareto optimal point of the problem, provided that the sectional curvature of the manifold is nonnegative and the multicriteria function is convex.

Keywords

Pareto optimality Multiobjective optimization Subgradient method Quasi-Féjer convergence 

Notes

Acknowledgements

The authors would like to extend their gratitude toward anonymous referees whose suggestions helped us to improve the presentation of this paper. The first author was partially supported by CNPq Grant 471815/2012-8, Project CAPES-MES-CUBA 226/2012, PROCAD-nf-UFG/UnB/IMPA, and FAPEG/CNPq. The second author was partially supported by CNPq GRANT 301625-2008 and PRONEX-Optimization (FAPERJ/CNPq).

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Universidade Federal de GoiásGoiâniaBrazil
  2. 2.Universidade Federal PiauíTeresinaBrazil

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