General descent method using w-distance. Application to emergence of habits following worthwhile moves
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- handle: 10670/1.cb23zs
- hal: hal-03135309
- doi: 10.23952/jnva.4.2020.2.09
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Antoine Soubeyran et al., « General descent method using w-distance. Application to emergence of habits following worthwhile moves », HAL-SHS : économie et finance, ID : 10.23952/jnva.4.2020.2.09
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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.