Weak Error Tolerance Criterion in Generalized Proximal Methods

Two inexact versions of a Bregman-function-based proximal method for nding a zero of a maximal monotone operator, suggested in [4] and [3], are considered. For a wide class of Bregman functions convergence of these methods is proved under an essentially weaker condition on the sequence of errors than in the original papers. Also the error criterion of a logarithmic-quadratic proximal method, developed in [1], is relaxed. For the methods mentioned only summability of the sequence of error vector norms is required.