Linear Convergence of Primal-Dual Gradient Methods and their Performance in Distributed Optimization
Optimization and Control
2020-01-17 v2
Abstract
In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear (exponential) convergence of the algorithm for smooth strongly-convex cost functions and study its relation to the non-incremental implementation. We also study the effect of the augmented Lagrangian penalty term on the performance of distributed optimization algorithms for the minimization of aggregate cost functions over multi-agent networks.
Cite
@article{arxiv.1904.01196,
title = {Linear Convergence of Primal-Dual Gradient Methods and their Performance in Distributed Optimization},
author = {Sulaiman A. Alghunaim and Ali H. Sayed},
journal= {arXiv preprint arXiv:1904.01196},
year = {2020}
}