Primal-dual incremental gradient method for nonsmooth and convex optimization problems

In this paper, we consider a nonsmooth convex finite-sum problem with conic constraint. To overcome the challenge of projecting onto constraint set and computing full (sub)gradient, introduce primal-dual incremental gradient scheme where only component function two constraints are used to update each sub-iteration in cyclic order. We demonstrate an asymptotic sublinear rate convergence terms suboptimality infeasibility which is improvement over state-of-the-art schemes setting. Numerical results suggest that proposed compares well competitive methods.