4,643 research outputs found
A cooperative conjugate gradient method for linear systems permitting multithread implementation of low complexity
This paper proposes a generalization of the conjugate gradient (CG) method
used to solve the equation for a symmetric positive definite matrix
of large size . The generalization consists of permitting the scalar control
parameters (= stepsizes in gradient and conjugate gradient directions) to be
replaced by matrices, so that multiple descent and conjugate directions are
updated simultaneously. Implementation involves the use of multiple agents or
threads and is referred to as cooperative CG (cCG), in which the cooperation
between agents resides in the fact that the calculation of each entry of the
control parameter matrix now involves information that comes from the other
agents. For a sufficiently large dimension , the use of an optimal number of
cores gives the result that the multithread implementation has worst case
complexity in exact arithmetic. Numerical experiments, that
illustrate the interest of theoretical results, are carried out on a multicore
computer.Comment: Expanded version of manuscript submitted to the IEEE-CDC 2012
(Conference on Decision and Control
Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms with Directed Gossip Communication
We study distributed optimization in networked systems, where nodes cooperate
to find the optimal quantity of common interest, x=x^\star. The objective
function of the corresponding optimization problem is the sum of private (known
only by a node,) convex, nodes' objectives and each node imposes a private
convex constraint on the allowed values of x. We solve this problem for generic
connected network topologies with asymmetric random link failures with a novel
distributed, decentralized algorithm. We refer to this algorithm as AL-G
(augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented
Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast
gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual
function. Dual variables are updated by the standard method of multipliers, at
a slow time scale. To update the primal variables, we propose a novel,
Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses
unidirectional gossip communication, only between immediate neighbors in the
network and is resilient to random link failures. For networks with reliable
communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian
broadcast gossiping) algorithm reduces communication, computation and data
storage cost. We prove convergence for all proposed algorithms and demonstrate
by simulations the effectiveness on two applications: l_1-regularized logistic
regression for classification and cooperative spectrum sensing for cognitive
radio networks.Comment: 28 pages, journal; revise
Distributed Maximum Likelihood Sensor Network Localization
We propose a class of convex relaxations to solve the sensor network
localization problem, based on a maximum likelihood (ML) formulation. This
class, as well as the tightness of the relaxations, depends on the noise
probability density function (PDF) of the collected measurements. We derive a
computational efficient edge-based version of this ML convex relaxation class
and we design a distributed algorithm that enables the sensor nodes to solve
these edge-based convex programs locally by communicating only with their close
neighbors. This algorithm relies on the alternating direction method of
multipliers (ADMM), it converges to the centralized solution, it can run
asynchronously, and it is computation error-resilient. Finally, we compare our
proposed distributed scheme with other available methods, both analytically and
numerically, and we argue the added value of ADMM, especially for large-scale
networks
The finite element machine: An experiment in parallel processing
The finite element machine is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described
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