General descent method using w-distance. Application to emergence of habits following worthwhile moves
Antoine Soubeyran, João Carlos O. Souza · Journal of Nonlinear and Variational Analysis · 2020
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.