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A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems

Author

Listed:
  • Glaydston de Carvalho Bento

    (IME - IME, Federal University of Goiás)

  • Sandro Dimy Barbosa Bitar

    (ICE - ICE, Federal University of Amazonas)

  • João Xavier da Cruz Neto

    (CCN, DM, - CCN, DM, Federal University of Piauí)

  • Antoine Soubeyran

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • João Carlos de Oliveira Souza

    (Federal University of Piauí)

Abstract

We consider the constrained multi-objective optimization problem of finding Pareto critical points of difference of convex functions. The new approach proposed by Bento et al. (SIAM J Optim 28:1104–1120, 2018) to study the convergence of the proximal point method is applied. Our method minimizes at each iteration a convex approximation instead of the (non-convex) objective function constrained to a possibly non-convex set which assures the vector improving process. The motivation comes from the famous Group Dynamic problem in Behavioral Sciences where, at each step, a group of (possible badly informed) agents tries to increase his joint payoff, in order to be able to increase the payoff of each of them. In this way, at each step, this ascent process guarantees the stability of the group. Some encouraging preliminary numerical results are reported.

Suggested Citation

  • Glaydston de Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier da Cruz Neto & Antoine Soubeyran & João Carlos de Oliveira Souza, 2020. "A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems," Post-Print hal-02351104, HAL.
    • Handle: RePEc:hal:journl:hal-02351104
    DOI: 10.1007/s10589-019-00139-0
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-02351104
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