Complexity Certification of a Distributed Augmented Lagrangian Method

Journal Article (Journal Article)

In this paper, we present complexity certification results for a distributed augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the accelerated distributed AL (ADAL) algorithm, which can handle the coupled linear constraints in a distributed manner based on local estimates of the AL. We show that the theoretical complexity of ADAL to reach an \epsilon-optimal solution both in terms of suboptimality and infeasibility is O(\frac{1}{\epsilon }) iterations. Moreover, we provide a valid upper bound for the optimal dual multiplier, which enables us to explicitly specify these complexity bounds. We also show how to choose the step-size parameter to minimize the bounds on the convergence rates. Finally, we discuss a motivating example, a model predictive control problem, involving a finite number of subsystems, which interact with each other via a general network.

Full Text

Duke Authors

Cited Authors

  • Lee, S; Chatzipanagiotis, N; Zavlanos, MM

Published Date

  • March 1, 2018

Published In

Volume / Issue

  • 63 / 3

Start / End Page

  • 827 - 834

International Standard Serial Number (ISSN)

  • 0018-9286

Digital Object Identifier (DOI)

  • 10.1109/TAC.2017.2747503

Citation Source

  • Scopus