1,785 research outputs found
On the Linear Convergence of the ADMM in Decentralized Consensus Optimization
In decentralized consensus optimization, a connected network of agents
collaboratively minimize the sum of their local objective functions over a
common decision variable, where their information exchange is restricted
between the neighbors. To this end, one can first obtain a problem
reformulation and then apply the alternating direction method of multipliers
(ADMM). The method applies iterative computation at the individual agents and
information exchange between the neighbors. This approach has been observed to
converge quickly and deemed powerful. This paper establishes its linear
convergence rate for decentralized consensus optimization problem with strongly
convex local objective functions. The theoretical convergence rate is
explicitly given in terms of the network topology, the properties of local
objective functions, and the algorithm parameter. This result is not only a
performance guarantee but also a guideline toward accelerating the ADMM
convergence.Comment: 11 figures, IEEE Transactions on Signal Processing, 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
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
Localization of Control Synthesis Problem for Large-Scale Interconnected System Using IQC and Dissipativity Theories
The synthesis problem for the compositional performance certification of
interconnected systems is considered. A fairly unified description of control
synthesis problem is given using integral quadratic constraints (IQC) and
dissipativity. Starting with a given large-scale interconnected system and a
global performance objective, an optimization problem is formulated to search
for admissible dissipativity properties of each subsystems. Local control laws
are then synthesized to certify the relevant dissipativity properties.
Moreover, the term localization is introduced to describe a finite collection
of syntheses problems, for the local subsystems, which are a feasibility
certificate for the global synthesis problem. Consequently, the problem of
localizing the global problem to a smaller collection of disjointed sets of
subsystems, called groups, is considered. This works looks promising as another
way of looking at decentralized control and also as a way of doing performance
specifications for components in a large-scale system
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