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

  • Glaydston de Carvalho Bento
  • Orizon Pereira Ferreira
  • Antoine Soubeyran
  • Valdinês Leite de Sousa Júnior
Article

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.

Keywords

Multi-objective Inexact proximal Group dynamic Distributive justice Behavioral sciences Variational rationality 

Mathematics Subject Classification

90C29 90C30 49M30 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Glaydston de Carvalho Bento
    • 1
  • Orizon Pereira Ferreira
    • 1
  • Antoine Soubeyran
    • 2
  • Valdinês Leite de Sousa Júnior
    • 1
  1. 1.IMEUniversidade Federal de GoiásGoiâniaBrazil
  2. 2.CNRS & EHESS, Aix-Marseille School of EconomicsAix-Marseille UniversityMarseilleFrance

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