Variable smoothing incremental aggregated gradient method for nonsmooth nonconvex regularized optimization

In this paper, we focus on the problem of minimizing the sum of nonconvex smooth component functions and a nonsmooth weakly convex function composed with a linear operator. One specific application is logistic regression problems with weakly convex regularizers that introduce better sparsity than the standard convex regularizers. Based on the Moreau envelope with a decreasing sequence of smoothing parameters as well as incremental aggregated gradient method, we propose a variable smoothing incremental aggregated gradient (VS-IAG) algorithm. We also prove a complexity of O(epsilon(-3)) to achieve an epsilon-approximate solution.