833 research outputs found
Distributed Model Predictive Consensus via the Alternating Direction Method of Multipliers
We propose a distributed optimization method for solving a distributed model
predictive consensus problem. The goal is to design a distributed controller
for a network of dynamical systems to optimize a coupled objective function
while respecting state and input constraints. The distributed optimization
method is an augmented Lagrangian method called the Alternating Direction
Method of Multipliers (ADMM), which was introduced in the 1970s but has seen a
recent resurgence in the context of dramatic increases in computing power and
the development of widely available distributed computing platforms. The method
is applied to position and velocity consensus in a network of double
integrators. We find that a few tens of ADMM iterations yield closed-loop
performance near what is achieved by solving the optimization problem
centrally. Furthermore, the use of recent code generation techniques for
solving local subproblems yields fast overall computation times.Comment: 7 pages, 5 figures, 50th Allerton Conference on Communication,
Control, and Computing, Monticello, IL, USA, 201
Fast ADMM Algorithm for Distributed Optimization with Adaptive Penalty
We propose new methods to speed up convergence of the Alternating Direction
Method of Multipliers (ADMM), a common optimization tool in the context of
large scale and distributed learning. The proposed method accelerates the speed
of convergence by automatically deciding the constraint penalty needed for
parameter consensus in each iteration. In addition, we also propose an
extension of the method that adaptively determines the maximum number of
iterations to update the penalty. We show that this approach effectively leads
to an adaptive, dynamic network topology underlying the distributed
optimization. The utility of the new penalty update schemes is demonstrated on
both synthetic and real data, including a computer vision application of
distributed structure from motion.Comment: 8 pages manuscript, 2 pages appendix, 5 figure
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