A proximal algorithm with quasi distance. Application to habit's formation

A Generalized Inexact Proximal Point Method for Nonsmooth Functions that Satisfies Kurdyka Lojasiewicz Inequality

“…In this paper, we show when, in a quasi metric space, an inexact proximal algorithm with a generalized perturbation term converges to a critical point of a objective function that fulfills the Kurdyka-Lojasiewicz inequality, depending on the curvature of the pertubation term. Our convergence analysis is an extension of the analysis due to Attouch and Bolte [1] and, more generally, due to Moreno et al [31], to an inexact setting of the proximal method, which is more suitable from the point of view of applications because, in the exact case, the proximal algorithm would transform an optimization problem in an infinite sequence of optimization problems. Actually, this is one usual criticism for exact proximal algorithms which is even stronger for behavioral applications.…”

“…Note that for different choices of and q, the worthwhile to change condition which defines the worthwhile to change set is a descent condition; see, for instance, [1,2,31]. This variational approach provides us an extra motivation to develop further the study of proximal algorithms where the perturbation term of the usual proximal point algorithm becomes a "curved enough" function of the quasi distance between two successive iterates.…”

“…The Method (4) is new and more adapted for applications in Behavioral Sciences. Moreover, it retrieves formulations that have recently been considered for nonconvex functions, see [1,31].…”

Um Algoritmo de Ponto Proximal Inexato para Programação Multiobjetivo

“…Uma de suas principais contribuições foi a introdução da aplicação quase-distância nos subproblemas regularizados do APP, que possui importantes aplicações em teoria da computação [3] e economia [8], entre outras. Sob certas hipóteses 1 azevedo@uft.edu.br 2 rgregor@ufrrj.br 2 razoáveis, mostraram a convergência do APP para soluções Pareto fraco e, devido a importância das soluções Pareto para as aplicações, exibiram uma classe de sequências que são geradas pelo algoritmo e que convergem para solução Pareto (em vez de Pareto fraco).…”

Proximal Point Method on Finslerian Manifolds and the “Effort–Accuracy” Trade-off

“…The general concept of costs to change in behavioral sciences ( economics, management, psychology) comes from Soubeyran [11,12]. See also Attouch-Soubeyran [14] and Moreno et al [39] for an interpretation as regularization terms for proximal algorithms.…”