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A Proximal Point Algorithm with Quasi-distance in Multi-objective Optimization

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Abstract

In this paper, we present a generalized vector-valued proximal point algorithm for convex and unconstrained multi-objective optimization problems. Our main contribution is the introduction of quasi-distance mappings in the regularized subproblems, which has important applications in the computer theory and economics, among others. By considering a certain class of quasi-distances, that are Lipschitz continuous and coercive in any of their arguments, we show that any sequence generated by our algorithm is bounded and its accumulation points are weak Pareto solutions.

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Acknowledgments

The authors thank the referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. Federal University of Tocantins, Tocantins, Brazil

    Rogério A. Rocha

  2. Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Paulo R. Oliveira

  3. Rural Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Ronaldo M. Gregório

  4. Federal University of Ceará, Ceará, Brazil

    Michael Souza

Authors
  1. Rogério A. Rocha
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  2. Paulo R. Oliveira
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  3. Ronaldo M. Gregório
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  4. Michael Souza
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Correspondence to Rogério A. Rocha.

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Rocha, R.A., Oliveira, P.R., Gregório, R.M. et al. A Proximal Point Algorithm with Quasi-distance in Multi-objective Optimization. J Optim Theory Appl 171, 964–979 (2016). https://doi.org/10.1007/s10957-016-1005-z

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  • DOI: https://doi.org/10.1007/s10957-016-1005-z

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