A Line Search Based Proximal Stochastic Gradient Algorithm with Dynamical Variance Reduction (vol 94, 23, 2023)

This file contains a revised version of the proofs of Theorems 3 and 4 of the paper [1]. In particular, a more correct argument is employed to obtain the inequality (A11) from (A10), provided that a stronger hypothesis on the sequence {epsilon(k)} is included. The practical implementation of the algorithm (Section 3) remains as it is and all the numerical experiments (Section 4) are still valid since the stronger hypothesis on {epsilon(k)} was already satisfied by the selected setting of the hyperparameters.