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arXiv · 1406.5403

A Primal-Dual Algorithmic Framework for Constrained Convex Minimization

Quoc Tran-Dinh·Volkan Cevher
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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.

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Quoc Tran-Dinh, Volkan Cevher. 2014-06-20. A Primal-Dual Algorithmic Framework for Constrained Convex Minimization. https://arxiv.org/abs/1406.5403

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