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