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A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds

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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.

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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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Authors and Affiliations

  1. Universidade Federal de Goiás, Goiânia, Brazil

    G. C. Bento

  2. Universidade Federal Piauí, Teresina, Brazil

    J. X. Cruz Neto

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  1. G. C. Bento
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Correspondence to G. C. Bento.

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Communicated by Alfredo Iusem.

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Bento, G.C., Cruz Neto, J.X. A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds. J Optim Theory Appl 159, 125–137 (2013). https://doi.org/10.1007/s10957-013-0307-7

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