262 research outputs found
D-ADMM: A Communication-Efficient Distributed Algorithm For Separable Optimization
We propose a distributed algorithm, named Distributed Alternating Direction
Method of Multipliers (D-ADMM), for solving separable optimization problems in
networks of interconnected nodes or agents. In a separable optimization problem
there is a private cost function and a private constraint set at each node. The
goal is to minimize the sum of all the cost functions, constraining the
solution to be in the intersection of all the constraint sets. D-ADMM is proven
to converge when the network is bipartite or when all the functions are
strongly convex, although in practice, convergence is observed even when these
conditions are not met. We use D-ADMM to solve the following problems from
signal processing and control: average consensus, compressed sensing, and
support vector machines. Our simulations show that D-ADMM requires less
communications than state-of-the-art algorithms to achieve a given accuracy
level. Algorithms with low communication requirements are important, for
example, in sensor networks, where sensors are typically battery-operated and
communicating is the most energy consuming operation.Comment: To appear in IEEE Transactions on Signal Processin
Distributed Optimization With Local Domains: Applications in MPC and Network Flows
In this paper we consider a network with nodes, where each node has
exclusive access to a local cost function. Our contribution is a
communication-efficient distributed algorithm that finds a vector
minimizing the sum of all the functions. We make the additional assumption that
the functions have intersecting local domains, i.e., each function depends only
on some components of the variable. Consequently, each node is interested in
knowing only some components of , not the entire vector. This allows
for improvement in communication-efficiency. We apply our algorithm to model
predictive control (MPC) and to network flow problems and show, through
experiments on large networks, that our proposed algorithm requires less
communications to converge than prior algorithms.Comment: Submitted to IEEE Trans. Aut. Contro
Distributed Basis Pursuit
We propose a distributed algorithm for solving the optimization problem Basis
Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear
system Ax = b and is used, for example, in compressed sensing for
reconstruction. Our algorithm solves BP on a distributed platform such as a
sensor network, and is designed to minimize the communication between nodes.
The algorithm only requires the network to be connected, has no notion of a
central processing node, and no node has access to the entire matrix A at any
time. We consider two scenarios in which either the columns or the rows of A
are distributed among the compute nodes. Our algorithm, named D-ADMM, is a
decentralized implementation of the alternating direction method of
multipliers. We show through numerical simulation that our algorithm requires
considerably less communications between the nodes than the state-of-the-art
algorithms.Comment: Preprint of the journal version of the paper; IEEE Transactions on
Signal Processing, Vol. 60, Issue 4, April, 201
A unified algorithmic approach to distributed optimization
We address general optimization problems formulated on networks. Each node in the network has a function, and the goal is to find a vec-tor x ∈ Rn that minimizes the sum of all the functions. We assume that each function depends on a set of components of x, not neces-sarily on all of them. This creates additional structure in the prob-lem, which can be captured by the classification scheme we develop. This scheme not only to enables us to design an algorithm that solves very general distributed optimization problems, but also allows us to categorize prior algorithms and applications. Our general-purpose algorithm shows a performance superior to prior algorithms, includ-ing algorithms that are application-specific. Index Terms — Distributed optimization, sensor networks 1
Processor Allocation for Optimistic Parallelization of Irregular Programs
Optimistic parallelization is a promising approach for the parallelization of
irregular algorithms: potentially interfering tasks are launched dynamically,
and the runtime system detects conflicts between concurrent activities,
aborting and rolling back conflicting tasks. However, parallelism in irregular
algorithms is very complex. In a regular algorithm like dense matrix
multiplication, the amount of parallelism can usually be expressed as a
function of the problem size, so it is reasonably straightforward to determine
how many processors should be allocated to execute a regular algorithm of a
certain size (this is called the processor allocation problem). In contrast,
parallelism in irregular algorithms can be a function of input parameters, and
the amount of parallelism can vary dramatically during the execution of the
irregular algorithm. Therefore, the processor allocation problem for irregular
algorithms is very difficult.
In this paper, we describe the first systematic strategy for addressing this
problem. Our approach is based on a construct called the conflict graph, which
(i) provides insight into the amount of parallelism that can be extracted from
an irregular algorithm, and (ii) can be used to address the processor
allocation problem for irregular algorithms. We show that this problem is
related to a generalization of the unfriendly seating problem and, by extending
Tur\'an's theorem, we obtain a worst-case class of problems for optimistic
parallelization, which we use to derive a lower bound on the exploitable
parallelism. Finally, using some theoretically derived properties and some
experimental facts, we design a quick and stable control strategy for solving
the processor allocation problem heuristically.Comment: 12 pages, 3 figures, extended version of SPAA 2011 brief announcemen
Characterising the temporal evolution of fixation in human post mortem brain via linear relaxometry modelling – a marker of cross-linking?
MRI-based biophysical models are typically validated by comparison to ex-vivo histology of fixed tissue. The fixation process itself and the accompanied autolysis processes strongly modify tissue composition, and lead to MR signal changes, making the validation of biophysical models for in vivo MRI particularly challenging. To better understand the temporal evolution of the fixation process within the whole brain and its influence on MRI parameters, we monitor the temporal evolution of the fixation process of a whole human post-mortem brain using the linear relaxometry model across 15 time-points comprised of one unfixed, in-situ MRI scan and 14 ex-vivo MRI scans at different stages of the fixation process (days 1-93)
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