Convex optimization

We consider resolving the nonsmooth convex optimization problem. We present a smoothed augmented Lagrangian framework for resolving such problems where the Lagrangian subproblems are $L_k$-smooth and $L_k$ is a known constant. By employing smoothed Augmented Lagrangian schemes for getting approximate solutions of such problems and a suitably defined dual update, rate statements are established for the primal sub-optimality and infeasibility.