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Generalized Inexact Proximal Algorithms: Routine’s Formation with Resistance to Change, Following Worthwhile Changes

Author

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  • G. C. Bento

    (Universidade Federal de Goiás)

  • A. Soubeyran

    (Aix-Marseille University (Aix-Marseille School of Economics))

Abstract

This paper shows how, in a quasi-metric space, an inexact proximal algorithm with a generalized perturbation term appears to be a nice tool for Behavioral Sciences (Psychology, Economics, Management, Game theory,...). More precisely, the new perturbation term represents an index of resistance to change, defined as a “curved enough” function of the quasi-distance between two successive iterates. Using this behavioral point of view, the present paper shows how such a generalized inexact proximal algorithm can modelize the formation of habits and routines in a striking way. This idea comes from a recent “variational rationality approach” of human behavior which links a lot of different theories of stability (habits, routines, equilibrium, traps,...) and changes (creations, innovations, learning and destructions,...) in Behavioral Sciences and a lot of concepts and algorithms in variational analysis.

Suggested Citation

  • G. C. Bento & A. Soubeyran, 2015. "Generalized Inexact Proximal Algorithms: Routine’s Formation with Resistance to Change, Following Worthwhile Changes," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 172-187, July.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:1:d:10.1007_s10957-015-0711-2
    DOI: 10.1007/s10957-015-0711-2
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    References listed on IDEAS

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    7. Fabián Flores-Bazán & Dinh The Luc & Antoine Soubeyran, 2012. "Maximal Elements Under Reference-Dependent Preferences with Applications to Behavioral Traps and Games," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 883-901, December.
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    9. Joao Xavier Cruz Neto & Paulo Roberto Oliveira & A. Soares Jr Pedro & Antoine Soubeyran, 2013. "Learning how to Play Nash, Potential Games and Alternating Minimization Method for Structured Nonconvex Problems on Riemannian Manifolds," Post-Print hal-01500875, HAL.
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    Cited by:

    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.
    2. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
    3. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Antoine Soubeyran & João Carlos Oliveira Souza, 2020. "A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems," Computational Optimization and Applications, Springer, vol. 75(1), pages 263-290, January.
    4. E. A. Papa Quiroz & A. Soubeyran & P. R. Oliveira, 2023. "Coercivity and generalized proximal algorithms: application—traveling around the world," Annals of Operations Research, Springer, vol. 321(1), pages 451-467, February.
    5. J. X. Cruz Neto & J. O. Lopes & A. Soubeyran & J. C. O. Souza, 2022. "Abstract regularized equilibria: application to Becker’s household behavior theory," Annals of Operations Research, Springer, vol. 316(2), pages 1279-1300, September.
    6. João Carlos O. Souza & Paulo Roberto Oliveira & Antoine Soubeyran, 2016. "Global convergence of a proximal linearized algorithm for difference of convex functions," Post-Print hal-01440298, HAL.

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