3,795 research outputs found
Distributed Interior-point Method for Loosely Coupled Problems
In this paper, we put forth distributed algorithms for solving loosely
coupled unconstrained and constrained optimization problems. Such problems are
usually solved using algorithms that are based on a combination of
decomposition and first order methods. These algorithms are commonly very slow
and require many iterations to converge. In order to alleviate this issue, we
propose algorithms that combine the Newton and interior-point methods with
proximal splitting methods for solving such problems. Particularly, the
algorithm for solving unconstrained loosely coupled problems, is based on
Newton's method and utilizes proximal splitting to distribute the computations
for calculating the Newton step at each iteration. A combination of this
algorithm and the interior-point method is then used to introduce a distributed
algorithm for solving constrained loosely coupled problems. We also provide
guidelines on how to implement the proposed methods efficiently and briefly
discuss the properties of the resulting solutions.Comment: Submitted to the 19th IFAC World Congress 201
Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal Decomposition
Large-scale interconnected uncertain systems commonly have large state and
uncertainty dimensions. Aside from the heavy computational cost of solving
centralized robust stability analysis techniques, privacy requirements in the
network can also introduce further issues. In this paper, we utilize IQC
analysis for analyzing large-scale interconnected uncertain systems and we
evade these issues by describing a decomposition scheme that is based on the
interconnection structure of the system. This scheme is based on the so-called
chordal decomposition and does not add any conservativeness to the analysis
approach. The decomposed problem can be solved using distributed computational
algorithms without the need for a centralized computational unit. We further
discuss the merits of the proposed analysis approach using a numerical
experiment.Comment: 3 figures. Submitted to the 19th IFAC world congres
Distributed Robust Stability Analysis of Interconnected Uncertain Systems
This paper considers robust stability analysis of a large network of
interconnected uncertain systems. To avoid analyzing the entire network as a
single large, lumped system, we model the network interconnections with
integral quadratic constraints. This approach yields a sparse linear matrix
inequality which can be decomposed into a set of smaller, coupled linear matrix
inequalities. This allows us to solve the analysis problem efficiently and in a
distributed manner. We also show that the decomposed problem is equivalent to
the original robustness analysis problem, and hence our method does not
introduce additional conservativeness.Comment: This paper has been accepted for presentation at the 51st IEEE
Conference on Decision and Control, Maui, Hawaii, 201
Robust Stability Analysis of Sparsely Interconnected Uncertain Systems
In this paper, we consider robust stability analysis of large-scale sparsely
interconnected uncertain systems. By modeling the interconnections among the
subsystems with integral quadratic constraints, we show that robust stability
analysis of such systems can be performed by solving a set of sparse linear
matrix inequalities. We also show that a sparse formulation of the analysis
problem is equivalent to the classical formulation of the robustness analysis
problem and hence does not introduce any additional conservativeness. The
sparse formulation of the analysis problem allows us to apply methods that rely
on efficient sparse factorization techniques, and our numerical results
illustrate the effectiveness of this approach compared to methods that are
based on the standard formulation of the analysis problem.Comment: Provisionally accepted to appear in IEEE Transactions on Automatic
Contro
W Plus Multiple Jets at the LHC with High Energy Jets
We study the production of a W boson in association with n hard QCD jets (for
n>=2), with a particular emphasis on results relevant for the Large Hadron
Collider (7 TeV and 8 TeV). We present predictions for this process from High
Energy Jets, a framework for all-order resummation of the dominant
contributions from wide-angle QCD emissions. We first compare predictions
against recent ATLAS data and then shift focus to observables and regions of
phase space where effects beyond NLO are expected to be large.Comment: 19 pages, 9 figure
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