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

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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.

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Acknowledgements

Funding was provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico (Grant Nos. 203360/2014–1, 305462/2014–8, 423737/2016-3, 310864/2017-8, 424169/2018-5) and Fundação de Amparo à Pesquisa do Estado de Goiás (PRONEN Grant No. 201710267000532). The authors wish to express their gratitude to the anonymous referees for their helpful comments.

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Authors and Affiliations

  1. IME, Federal University of Goiás, Goiânia, Brazil

    Glaydston de Carvalho Bento

  2. ICE, Federal University of Amazonas, Manaus, AM, Brazil

    Sandro Dimy Barbosa Bitar

  3. CCN, DM, Federal University of Piauí, Teresina, PI, Brazil

    João Xavier da Cruz Neto & João Carlos de Oliveira Souza

  4. CNRS and EHESS, Aix-Marseille University (Aix-Marseille School of Economics), Aix-en-Provence, France

    Antoine Soubeyran

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  1. Glaydston de Carvalho Bento
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  3. João Xavier da Cruz Neto
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  5. João Carlos de Oliveira Souza
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Correspondence to João Carlos de Oliveira Souza.

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de Carvalho Bento, G., Bitar, S.D.B., da Cruz Neto, J.X. et al. A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems. Comput Optim Appl 75, 263–290 (2020). https://doi.org/10.1007/s10589-019-00139-0

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