A Primal-Dual Algorithmic Framework for Constrained Convex Minimization
We 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.
Keywords: Primal-dual method ; optimal first-order method ; augmented Lagrangian ; alternating direction method of multipliers ; separable convex minimization ; monotropic programming ; parallel and distributed algorithm
This manuscript has just submitted for publication
Record created on 2014-06-20, modified on 2016-08-09