993 research outputs found
A Convergence Result for Asynchronous Algorithms and Applications
We give in this paper a convergence result concerning parallel asynchronous
algorithm with bounded delays to solve a nonlinear fixed point problems. This
result is applied to calculate the solution of a strongly monotone operator.
Special cases of these operators are used to solve some problems related to
convex analysis like minimization of functionals, calculus of saddle point and
variational inequality problem
On the Convergence Analysis of Asynchronous Distributed Quadratic Programming via Dual Decomposition
In this paper, we analyze the convergence as well as the rate of convergence
of asynchronous distributed quadratic programming (QP) with dual decomposition
technique. In general, distributed optimization requires synchronization of
data at each iteration step due to the interdependency of data. This
synchronization latency may incur a large amount of waiting time caused by an
idle process during computation. We aim to attack this synchronization penalty
in distributed QP problems by implementing asynchronous update of dual
variable. The price to pay for adopting asynchronous computing algorithms is
unpredictability of the solution, resulting in a tradeoff between speedup and
accuracy. Thus, the convergence to an optimal solution is not guaranteed owing
to the stochastic behavior of asynchrony. In this paper, we employ the switched
system framework as an analysis tool to investigate the convergence of
asynchronous distributed QP. This switched system will facilitate analysis on
asynchronous distributed QP with dual decomposition, providing necessary and
sufficient conditions for the mean square convergence. Also, we provide an
analytic expression for the rate of convergence through the switched system,
which enables performance analysis of asynchronous algorithms as compared with
synchronous case. To verify the validity of the proposed methods, numerical
examples are presented with an implementation of asynchronous parallel QP using
OpenMP
Scheduled-Asynchronous Distributed Algorithm for Optimal Power Flow
Optimal power flow (OPF) problems are non-convex and large-scale optimization
problems with important applications in power networks. This paper proposes the
scheduled-asynchronous algorithm to solve a distributed semidefinite
programming (SDP) formulation of the OPF problem. In this formulation, every
agent seeks to solve a local optimization with its own cost function, physical
constraints on its nodal power injection, voltage, and power flow of the lines
it is connected to, and decision constraints on variables shared with neighbors
to ensure consistency of the obtained solution. In the scheduled-asynchronous
algorithm, every pair of connected nodes in the electrical network update their
local variables in an alternating fashion. This strategy is asynchronous, in
the sense that no clock synchronization is required, and relies on an
orientation of the electrical network that prescribes the precise ordering of
node updates. We establish the asymptotic convergence properties to the
primal-dual optimizer when the orientation is acyclic. Given the dependence of
the convergence rate on the network orientation, we also develop a distributed
graph coloring algorithm that finds an orientation with diameter at most five
for electrical networks with geometric degree distribution. Simulations
illustrate our results on various IEEE bus test cases
Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs
We study the Parallel Replica Dynamics in a general setting. We introduce a
trajectory fragment framework that can be used to design and prove consistency
of Parallel Replica algorithms for generic Markov processes. We use our
framework to formulate a novel condition that guarantees an asynchronous
algorithm is consistent. Exploiting this condition and our trajectory fragment
framework, we present new synchronous and asynchronous Parallel Replica
algorithms for piecewise deterministic Markov processes.Comment: 32 pages, 9 figure
Asynchronous Distributed Power Control of Multi-Microgrid Systems Based on the Operator Splitting Approach
Forming (hybrid) AC/DC microgrids (MGs) has become a promising manner for the
interconnection of various kinds of distributed generators that are inherently
AC or DC electric sources. This paper addresses the distributed asynchronous
power control problem of hybrid microgrids, considering imperfect communication
due to non-identical sampling rates and communication delays. To this end, we
first formulate the optimal power control problem of MGs and devise a
synchronous algorithm. Then, we analyze the impact of asynchrony on optimal
power control and propose an asynchronous iteration algorithm based on the
synchronous version. By introducing a random clock at each iteration, different
types of asynchrony are fitted into a unified framework, where the asynchronous
algorithm is converted into a fixed-point problem based on the operator
splitting method, leading to a convergence proof. We further provide an upper
bound estimation of the time delay in the communication. Moreover, the
real-time implementation of the proposed algorithm in both AC and DC MGs is
introduced. By taking the power system as a solver, the controller is
simplified by reducing one order and the power loss can be considered. Finally,
a benchmark MG is utilized to verify the effectiveness and advantages of the
proposed algorithm
Methods of robustness analysis for Boolean models of gene control networks
As a discrete approach to genetic regulatory networks, Boolean models provide
an essential qualitative description of the structure of interactions among
genes and proteins. Boolean models generally assume only two possible states
(expressed or not expressed) for each gene or protein in the network as well as
a high level of synchronization among the various regulatory processes. In this
paper, we discuss and compare two possible methods of adapting qualitative
models to incorporate the continuous-time character of regulatory networks. The
first method consists of introducing asynchronous updates in the Boolean model.
In the second method, we adopt the approach introduced by L. Glass to obtain a
set of piecewise linear differential equations which continuously describe the
states of each gene or protein in the network. We apply both methods to a
particular example: a Boolean model of the segment polarity gene network of
Drosophila melanogaster. We analyze the dynamics of the model, and provide a
theoretical characterization of the model's gene pattern prediction as a
function of the timescales of the various processes.Comment: 29 pages, 8 figures, accepted in IEE Proc. Systems Biolog
Asynchronous Algorithms for Solving Linear Programs
In this paper we design and analyze algorithms for asynchronously solving
linear programs using nonlinear signal processing structures. In particular, we
discuss a general procedure for generating these structures such that a
fixed-point of the structure is within a change of basis the minimizer of an
associated linear program. We discuss methods for organizing the computation
into distributed implementations and provide a treatment of convergence. The
presented algorithms are accompanied by numerical simulations of the Chebyshev
center and basis pursuit problems
Asynchronous Optimization Over Heterogeneous Networks via Consensus ADMM
This paper considers the distributed optimization of a sum of locally
observable, non-convex functions. The optimization is performed over a
multi-agent networked system, and each local function depends only on a subset
of the variables. An asynchronous and distributed alternating directions method
of multipliers (ADMM) method that allows the nodes to defer or skip the
computation and transmission of updates is proposed in the paper. The proposed
algorithm utilizes different approximations in the update step, resulting in
proximal and majorized ADMM variants. Both variants are shown to converge to a
local minimum, under certain regularity conditions. The proposed asynchronous
algorithms are also applied to the problem of cooperative localization in
wireless ad hoc networks, where it is shown to outperform the other
state-of-the-art localization algorithms.Comment: Submitted to Transactions on signal and information processing over
Network
A Switched Dynamical System Framework for Analysis of Massively Parallel Asynchronous Numerical Algorithms
In the near future, massively parallel computing systems will be necessary to
solve computation intensive applications. The key bottleneck in massively
parallel implementation of numerical algorithms is the synchronization of data
across processing elements (PEs) after each iteration, which results in
significant idle time. Thus, there is a trend towards relaxing the
synchronization and adopting an asynchronous model of computation to reduce
idle time. However, it is not clear what is the effect of this relaxation on
the stability and accuracy of the numerical algorithm. In this paper we present
a new framework to analyze such algorithms. We treat the computation in each PE
as a dynamical system and model the asynchrony as stochastic switching. The
overall system is then analyzed as a switched dynamical system. However,
modeling of massively parallel numerical algorithms as switched dynamical
systems results in a very large number of modes, which makes current analysis
tools available for such systems computationally intractable. We develop new
techniques that circumvent this scalability issue. The framework is presented
on a one-dimensional heat equation as a case study and the proposed analysis
framework is verified by solving the partial differential equation (PDE) in a
GPU machine, with asynchronous
communication between cores.Comment: ACC 201
Simple CHT: A New Derivation of the Weakest Failure Detector for Consensus
The paper proposes an alternative proof that Omega, an oracle that outputs a
process identifier and guarantees that eventually the same correct process
identifier is output at all correct processes, provides minimal information
about failures for solving consensus in read-write shared-memory systems: every
oracle that gives enough failure information to solve consensus can be used to
implement Omega.
Unlike the original proof by Chandra, Hadzilacos and Toueg (CHT), the proof
presented in this paper builds upon the very fact that 2-process wait-free
consensus is impossible. Also, since the oracle that is used to implement can
solve consensus, the implementation is allowed to directly access consensus
objects. As a result, the proposed proof is shorter and conceptually simpler
than the original one
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