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Volume 4, Issue 2, 1 August 2020, Pages 285-300
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.
How to Cite this Article:
Antoine Soubeyran, João Carlos de O. Souza, General descent method using w-distance. Application to emergence of habits following worthwhile moves, J. Nonlinear Var. Anal. 4 (2020), 285-300.