期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 63, 期 3, 页码 827-834出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2017.2747503
关键词
Augmented Lagrangian (AL) methods; computational complexity; distributed model predictive control (MPC)
资金
- NSF [1261828]
- ONR [N000141410479]
- Division Of Computer and Network Systems
- Direct For Computer & Info Scie & Enginr [1261828] Funding Source: National Science Foundation
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(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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