Lipschitz-Free Mirror Descent Methods for Non-Smooth Optimization Problems

The part of the analysis of the convergence rate of the mirror descent method that is connected with the adaptive time-varying step size rules due to Alkousa et al. (MOTOR 2024, pp. 3-18) is corrected. Moreover, a Lipschitz-free mirror descent method that achieves weak ergodic convergence is presented, generalizing the convergence results of the mirror descent method in the absence of the Lipschitz assumption.