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

Antoine Soubeyran (1) , João Carlos O. Souza (2)

1 AMSE - Aix-Marseille Sciences Economiques
2 Federal University of Piauí

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.

Mots clés: descent methods; Kurdyka-Łojasiewicz inequality; w-distance; habits; variational rationality

Domaines: Economies et finances

Antoine Soubeyran, João Carlos O. Souza. General descent method using w-distance. Application to emergence of habits following worthwhile moves. Journal of Nonlinear and Variational Analysis, 2020, 4 (2), pp.285-300. ⟨10.23952/jnva.4.2020.2.09⟩. ⟨hal-03135309⟩