# A Primal-Dual Algorithmic Framework for Constrained Convex Minimization

arXiv: https://arxiv.org/abs/1406.5403 · HTML: https://mlsanity.com/paper/1406.5403/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2014.

## Built on by (most cited first, 1 of 1)

- [Damped Proximal Augmented Lagrangian Method for weakly-Convex Problems with Convex Constraints](https://mlsanity.com/paper/2311.09065/) (2023)

## Abstract (arXiv)

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.