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Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm

Author

Listed:
  • Glaydston Carvalho Bento

    (UFG - Universidade Federal de Goiás [Goiânia])

  • João Xavier da Cruz Neto

    (UFPI - Universidade Federal do Piauí)

  • L. Meireles

    (IFGOIANO - Instituto Federal Goiano = Goiano Federal Institute)

  • 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)

Abstract

In this paper we introduce a definition of approximate Pareto efficient solution as well as a necessary condition for such solutions in the multiobjective setting on Riemannian manifolds. We also propose an inexact proximal point method for nonsmooth multiobjective optimization in the Riemannian context by using the notion of approximate solution. The main convergence result ensures that each cluster point (if any) of any sequence generated by the method is a Pareto critical point. Furthermore, when the problem is convex on a Hadamard manifold, full convergence of the method for a weak Pareto efficient solution is obtained. As an application, we show how a Pareto critical point can be reached as a limit of traps in the context of the variational rationality approach of stay and change human dynamics.

Suggested Citation

  • Glaydston Carvalho Bento & João Xavier da Cruz Neto & L. Meireles & Antoine Soubeyran, 2022. "Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm," Post-Print hal-03680291, HAL.
    • Handle: RePEc:hal:journl:hal-03680291
    DOI: 10.1007/s10479-022-04719-y
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-03680291
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    Cited by:

    1. G. C. Bento & J. X. Cruz Neto & J. O. Lopes & B. S. Mordukhovich & P. R. Silva Filho, 2025. "A refined proximal algorithm for nonconvex multiobjective optimization in Hilbert spaces," Journal of Global Optimization, Springer, vol. 92(1), pages 187-203, May.

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