Inexact Version of the Entropic Proximal Point Algorithm

Abstract

In this paper, we study an inexact version of the entropic proximal point algorithm defined by $$ x^{k} \in \varepsilon_{k} - Argmin \lbrace f(.) + \lambda_{k}^{-1} D_{h} ( ., x^{k-1} ) \rbrace.$$ This study recovers the most of the algotithms of the proximal point.