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A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem

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Listed:
  • J. X. Cruz Neto

    (Universidade Federal do Piauí)

  • P. R. Oliveira

    (Universidade Federal do Rio de Janeiro)

  • A. Soubeyran

    (Aix-Marseille University (Aix-Marseille School of Economics), CNRS & EHESS)

  • J. C. O. Souza

    (Universidade Federal do Piauí)

Abstract

The purpose of this paper is twofold. First, we examine convergence properties of an inexact proximal point method with a quasi distance as a regularization term in order to find a critical point (in the sense of Toland) of a DC function (difference of two convex functions). Global convergence of the sequence and some convergence rates are obtained with additional assumptions. Second, as an application and its inspiration, we study in a dynamic setting, the very important and difficult problem of the limit of the firm and the time it takes to reach it (maturation time), when increasing returns matter in the short run. Both the formalization of the critical size of the firm in term of a recent variational rationality approach of human dynamics and the speed of convergence results are new in Behavioral Sciences.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:289:y:2020:i:2:d:10.1007_s10479-018-3104-8
    DOI: 10.1007/s10479-018-3104-8
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    Cited by:

    1. Antoine Soubeyran, 2022. "Variational rationality. Self regulation success as a succession of worthwhile moves that make sufficient progress," Working Papers hal-04041238, HAL.
    2. Majid Fakhar & Mohammadreza Khodakhah & Ali Mazyaki & Antoine Soubeyran & Jafar Zafarani, 2022. "Variational rationality, variational principles and the existence of traps in a changing environment," Journal of Global Optimization, Springer, vol. 82(1), pages 161-177, January.
    3. 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.
    4. Antoine Soubeyran, 2023. "Variational rationality. Self regulation success as a succession of worthwhile moves that make sufficient progress," AMSE Working Papers 2307, Aix-Marseille School of Economics, France.

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