A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes

  • Kely D. V. Villacorta
  • Paulo R. Oliveira
  • Antoine Soubeyran


Multiobjective optimization has a significant number of real-life applications. For this reason, in this paper we consider the problem of finding Pareto critical points for unconstrained multiobjective problems and present a trust-region method to solve it. Under certain assumptions, which are derived in a very natural way from assumptions used to establish convergence results of the scalar trust-region method, we prove that our trust-region method generates a sequence which converges in the Pareto critical way. This means that our generalized marginal function, which generalizes the norm of the gradient for the multiobjective case, converges to zero. In the last section of this paper, we give an application to satisficing processes in Behavioral Sciences. Multiobjective trust-region methods appear to be remarkable specimens of much more abstract satisficing processes, based on “variational rationality” concepts. One of their important merits is to allow for efficient computations. This is a striking result in Behavioral Sciences.


Trust-region methods Unconstrained multiobjective problem Pareto critical point Satisficing process Worthwhile change Variational rationality 



This work was partially supported by CNPq—Brasil. The authors wish to thank the anonymous referees for carefully reading the paper and providing valuable comments and suggestions which helped them improve the presentation.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Kely D. V. Villacorta
    • 1
  • Paulo R. Oliveira
    • 2
    • 3
  • Antoine Soubeyran
    • 4
  1. 1.DCC-CIFederal University of ParaíbaJoão Pessoa-ParaíbaBrazil
  2. 2.PESC-COPPEFederal University of Rio de JaneiroRio de JaneiroBrazil
  3. 3.Centro de TecnologiaCidade UniversitáriaRio de JaneiroBrazil
  4. 4.Aix-Marseille University (Aix-Marseille School of Economics)CNRS & EHESS, Chateau LafargeLes MillesFrance

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