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

Antoine Soubeyran and João Carlos O. Souza
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João Carlos O. Souza: Federal University of Piauí

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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.

Keywords: descent methods; Kurdyka-Łojasiewicz inequality; w-distance; habits; variational rationality (search for similar items in EconPapers)
Date: 2020-08
Note: View the original document on HAL open archive server: https://amu.hal.science/hal-03135309
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Published in Journal of Nonlinear and Variational Analysis, 2020, 4 (2), pp.285-300. ⟨10.23952/jnva.4.2020.2.09⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03135309

DOI: 10.23952/jnva.4.2020.2.09

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