On the convergence of a Block-Coordinate Incremental Gradient method

In this paper, we study the convergence of a block-coordinate incremental gradient method. Under some specific assumptions on the objective function, we prove that the block-coordinate incremental gradient method can be seen as a gradient method with errors and convergence can be proved by showing the error at each iteration satisfies some standard conditions. Thus, we can prove convergence towards stationary points when the block incremental gradient method is coupled with a diminishing stepsize and towards an ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-approximate solution when a bounded away from zero stepsize is employed.