Complexity Certification of a Distributed Augmented Lagrangian Method
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.
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Related Subject Headings
- Industrial Engineering & Automation
- 4007 Control engineering, mechatronics and robotics
- 0913 Mechanical Engineering
- 0906 Electrical and Electronic Engineering
- 0102 Applied Mathematics
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Industrial Engineering & Automation
- 4007 Control engineering, mechatronics and robotics
- 0913 Mechanical Engineering
- 0906 Electrical and Electronic Engineering
- 0102 Applied Mathematics