A Primal-Dual Algorithmic Framework for Constrained Convex Minimization
Abstract: 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.
Category 1: Convex and Nonsmooth Optimization
Citation: Tech. Report, EPFL-REPORT-199844
Entry Submitted: 06/22/2014
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