Tran Dinh, QuocCevher, Volkan2014-06-202014-06-202014-06-202014https://infoscience.epfl.ch/handle/20.500.14299/104549We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov's excessive gap technique in a structured fashion and unifies it with smoothing and primal-dual methods. For instance, through the choices of a dual smoothing strategy and a center point, our framework subsumes decomposition algorithms, augmented Lagrangian as well as the alternating direction method-of-multipliers methods as its special cases, and provides optimal convergence rates on the primal objective residual as well as the primal feasibility gap of the iterates for all.Primal-dual methodoptimal first-order methodaugmented Lagrangianalternating direction method of multipliersseparable convex minimizationmonotropic programmingparallel and distributed algorithmtext::report