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A modified proximal point method for DC functions on Hadamard manifolds

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Abstract

We study the convergence of a modified proximal point method for DC functions in Hadamard manifolds. We use the iteration computed by the proximal point method for DC function extended to the Riemannian context by Souza and Oliveira (J Glob Optim 63:797–810, 2015) to define a descent direction which improves the convergence of the method. Our method also accelerates the classical proximal point method for convex functions. We illustrate our results with some numerical experiments.

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Acknowledgements

This study was funded by Conselho Nacional de Desenvolvimento Científico e Tecnológico (Grant Nos. 305462/2014-8, 424169/2018-5, 302678/2017-4, 308330/2018-8) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior. The authors wish to express their gratitude to the anonymous referees for their helpful comments.

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Authors and Affiliations

  1. COPPE-PESC, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Yldenilson Torres Almeida & Paulo Roberto Oliveira

  2. CCN, DM, Federal University of Piauí, Teresina, PI, Brazil

    João Xavier da Cruz Neto & João Carlos de Oliveira Souza

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  1. Yldenilson Torres Almeida
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  2. João Xavier da Cruz Neto
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  3. Paulo Roberto Oliveira
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  4. João Carlos de Oliveira Souza
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Correspondence to João Carlos de Oliveira Souza.

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Almeida, Y.T., da Cruz Neto, J.X., Oliveira, P.R. et al. A modified proximal point method for DC functions on Hadamard manifolds. Comput Optim Appl 76, 649–673 (2020). https://doi.org/10.1007/s10589-020-00173-3

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