726 research outputs found
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
On Cooperative Beamforming Based on Second-Order Statistics of Channel State Information
Cooperative beamforming in relay networks is considered, in which a source
transmits to its destination with the help of a set of cooperating nodes. The
source first transmits locally. The cooperating nodes that receive the source
signal retransmit a weighted version of it in an amplify-and-forward (AF)
fashion. Assuming knowledge of the second-order statistics of the channel state
information, beamforming weights are determined so that the signal-to-noise
ratio (SNR) at the destination is maximized subject to two different power
constraints, i.e., a total (source and relay) power constraint, and individual
relay power constraints. For the former constraint, the original problem is
transformed into a problem of one variable, which can be solved via Newton's
method. For the latter constraint, the original problem is transformed into a
homogeneous quadratically constrained quadratic programming (QCQP) problem. In
this case, it is shown that when the number of relays does not exceed three the
global solution can always be constructed via semidefinite programming (SDP)
relaxation and the matrix rank-one decomposition technique. For the cases in
which the SDP relaxation does not generate a rank one solution, two methods are
proposed to solve the problem: the first one is based on the coordinate descent
method, and the second one transforms the QCQP problem into an infinity norm
maximization problem in which a smooth finite norm approximation can lead to
the solution using the augmented Lagrangian method.Comment: 30 pages, 9 figure
Optimal mistuning for enhanced aeroelastic stability of transonic fans
An inverse design procedure was developed for the design of a mistuned rotor. The design requirements are that the stability margin of the eigenvalues of the aeroelastic system be greater than or equal to some minimum stability margin, and that the mass added to each blade be positive. The objective was to achieve these requirements with a minimal amount of mistuning. Hence, the problem was posed as a constrained optimization problem. The constrained minimization problem was solved by the technique of mathematical programming via augmented Lagrangians. The unconstrained minimization phase of this technique was solved by the variable metric method. The bladed disk was modelled as being composed of a rigid disk mounted on a rigid shaft. Each of the blades were modelled with a single tosional degree of freedom
Distributed reactive power feedback control for voltage regulation and loss minimization
We consider the problem of exploiting the microgenerators dispersed in the
power distribution network in order to provide distributed reactive power
compensation for power losses minimization and voltage regulation. In the
proposed strategy, microgenerators are smart agents that can measure their
phasorial voltage, share these data with the other agents on a cyber layer, and
adjust the amount of reactive power injected into the grid, according to a
feedback control law that descends from duality-based methods applied to the
optimal reactive power flow problem. Convergence to the configuration of
minimum losses and feasible voltages is proved analytically for both a
synchronous and an asynchronous version of the algorithm, where agents update
their state independently one from the other. Simulations are provided in order
to illustrate the performance and the robustness of the algorithm, and the
innovative feedback nature of such strategy is discussed
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