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Inexact Multi-Objective Local Search Proximal Algorithms: Application to Group Dynamic and Distributive Justice Problems

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Abstract

We introduce and examine an inexact multi-objective proximal method with a proximal distance as the perturbation term. Our algorithm utilizes a local search descent process that eventually reaches a weak Pareto optimum of a multi-objective function, whose components are the maxima of continuously differentiable functions. Our algorithm gives a new formulation and resolution of the following important distributive justice problem in the context of group dynamics: In each period, if a group creates a cake, the problem is, for each member, to get a high enough share of this cake; if this is not possible, then it is better to quit, breaking the stability of the group.

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Acknowledgements

The work was supported by CAPES, CNPq, MathAmSud (CAPES) 88881.117595/2016-01 and the ANR GREEN-Econ research project (ANR-16-CE03-0005).

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Authors and Affiliations

  1. IME, Universidade Federal de Goiás, Goiânia, GO, 74001-970, Brazil

    Glaydston de Carvalho Bento, Orizon Pereira Ferreira & Valdinês Leite de Sousa Júnior

  2. CNRS & EHESS, Aix-Marseille School of Economics, Aix-Marseille University, Marseille, France

    Antoine Soubeyran

Authors
  1. Glaydston de Carvalho Bento
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  2. Orizon Pereira Ferreira
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  3. Antoine Soubeyran
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  4. Valdinês Leite de Sousa Júnior
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Correspondence to Valdinês Leite de Sousa Júnior.

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Communicated by Alfredo N. Iusem.

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Bento, G.d.C., Ferreira, O.P., Soubeyran, A. et al. Inexact Multi-Objective Local Search Proximal Algorithms: Application to Group Dynamic and Distributive Justice Problems. J Optim Theory Appl 177, 181–200 (2018). https://doi.org/10.1007/s10957-018-1258-9

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  • DOI: https://doi.org/10.1007/s10957-018-1258-9

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