Stochastic subgradient algorithm for nonsmooth nonconvex optimization

In this paper, we study on a stochastic subgradient algorithm for the finite-sum optimization problems where the functions are not necessarily convex and smooth and we use a weak subgradient of only one function at each iteration. We then analyze the convergence properties of the stochastic weak subgradient algorithm (SWSA). In addition, we focus on the problem that arises in the semi-supervised machine learning (SSML) problem where all the functions in the problem are not smooth and convex, and we propose an algorithm called WS-SSML to compute a weak subgradient of these functions in SSML. Finally, we solve the SSML problem using the data sets from the literature and we compare our results. We can conclude that SWSA with WS-SSML works well in practice.