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General descent method using w-distance. Application to emergence of habits following worthwhile moves

Author

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  • 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)

  • João Carlos O. Souza

    (Federal University of Piauí)

Abstract

In this paper, we extend the general descent method proposed by Attouch, Bolte and Svaiter [Math. Program. 137 (2013), 91-129] to deal with possible asymmetric like-distances. Using a w-distance as regularization term our results guarantee the convergence of bounded sequences, under the assumption that the objective function satisfies the Kurdyka-Łojasiewicz inequality. In particular, it improves some existing works on proximal point methods with quasi-distance as regularization term because we prove convergence of bounded sequences without any additional assumption on the w-distance unlike it have been done with quasi-distances. The last section gives an application relative to the emergence of habits after a succession of worthwhile moves which balance motivation and resistance to move.

Suggested Citation

  • Antoine Soubeyran & João Carlos O. Souza, 2020. "General descent method using w-distance. Application to emergence of habits following worthwhile moves," Post-Print hal-03135309, HAL.
    • Handle: RePEc:hal:journl:hal-03135309
    DOI: 10.23952/jnva.4.2020.2.09
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-03135309
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    Cited by:

    1. 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.

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