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

Author

Listed:
  • Glaydston de Carvalho Bento

    (Universidade Federal de Goiás)

  • Orizon Pereira Ferreira

    (Universidade Federal de Goiás)

  • Antoine Soubeyran

    (Aix-Marseille University)

  • Valdinês Leite de Sousa Júnior

    (Universidade Federal de Goiás)

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.

Suggested Citation

  • Glaydston de Carvalho Bento & Orizon Pereira Ferreira & Antoine Soubeyran & Valdinês Leite de Sousa Júnior, 2018. "Inexact Multi-Objective Local Search Proximal Algorithms: Application to Group Dynamic and Distributive Justice Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 181-200, April.
    • Handle: RePEc:spr:joptap:v:177:y:2018:i:1:d:10.1007_s10957-018-1258-9
    DOI: 10.1007/s10957-018-1258-9
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    1. Glaydston Carvalho Bento & João Xavier Cruz Neto & Antoine Soubeyran & Valdinês Leite Sousa Júnior, 2016. "Dual Descent Methods as Tension Reduction Systems," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 209-227, October.
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    Cited by:

    1. G. C. Bento & J. X. Cruz Neto & L. V. Meireles & A. Soubeyran, 2022. "Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm," Annals of Operations Research, Springer, vol. 316(2), pages 1425-1443, September.

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