Proximal point method for pointwise convergent sucessions of Bregman functions (Publicaciones en Ciencias y Tecnología, 2018)
A generalization of the classical proximal point method and the method of proximal point with Bregman distances is developed under conditions of convexity. Starting from an arbitrary punctually convergent sucession of Bregman functions, our method allows both the generalization to the classic cases that have been developed for a fixed Bregman function and the addition of properties that regulate the behavior of the succession of Bregman distances. Thus, a method that converges to the minimizer of the objective function is obtained.
Keywords: proximal point method; Bregman distances; function successions; Bregman