35,963 research outputs found
A unified framework for solving a general class of conditional and robust set-membership estimation problems
In this paper we present a unified framework for solving a general class of
problems arising in the context of set-membership estimation/identification
theory. More precisely, the paper aims at providing an original approach for
the computation of optimal conditional and robust projection estimates in a
nonlinear estimation setting where the operator relating the data and the
parameter to be estimated is assumed to be a generic multivariate polynomial
function and the uncertainties affecting the data are assumed to belong to
semialgebraic sets. By noticing that the computation of both the conditional
and the robust projection optimal estimators requires the solution to min-max
optimization problems that share the same structure, we propose a unified
two-stage approach based on semidefinite-relaxation techniques for solving such
estimation problems. The key idea of the proposed procedure is to recognize
that the optimal functional of the inner optimization problems can be
approximated to any desired precision by a multivariate polynomial function by
suitably exploiting recently proposed results in the field of parametric
optimization. Two simulation examples are reported to show the effectiveness of
the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic
Control (2014
A two-phase gradient method for quadratic programming problems with a single linear constraint and bounds on the variables
We propose a gradient-based method for quadratic programming problems with a
single linear constraint and bounds on the variables. Inspired by the GPCG
algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and
G. Toraldo, SIAM J. Optim. 1, 1991], our approach alternates between two phases
until convergence: an identification phase, which performs gradient projection
iterations until either a candidate active set is identified or no reasonable
progress is made, and an unconstrained minimization phase, which reduces the
objective function in a suitable space defined by the identification phase, by
applying either the conjugate gradient method or a recently proposed spectral
gradient method. However, the algorithm differs from GPCG not only because it
deals with a more general class of problems, but mainly for the way it stops
the minimization phase. This is based on a comparison between a measure of
optimality in the reduced space and a measure of bindingness of the variables
that are on the bounds, defined by extending the concept of proportioning,
which was proposed by some authors for box-constrained problems. If the
objective function is bounded, the algorithm converges to a stationary point
thanks to a suitable application of the gradient projection method in the
identification phase. For strictly convex problems, the algorithm converges to
the optimal solution in a finite number of steps even in case of degeneracy.
Extensive numerical experiments show the effectiveness of the proposed
approach.Comment: 30 pages, 17 figure
Adapting the interior point method for the solution of linear programs on high performance computers
In this paper we describe a unified algorithmic framework for the interior point method (IPM) of solving Linear Programs (LPs) which allows us to adapt it over a range of high performance computer architectures. We set out the reasons as to why IPM makes better use of high performance computer architecture than the sparse simplex method. In the inner iteration of the IPM a search direction is computed using Newton or higher order methods. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system and the design of data structures to take advantage of coarse grain parallel and massively parallel computer architectures are considered in detail. Finally, we present experimental results of solving NETLIB test problems on examples of these architectures and put forward arguments as to why integration of the system within sparse simplex is beneficial
Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings
We tackle the multi-party speech recovery problem through modeling the
acoustic of the reverberant chambers. Our approach exploits structured sparsity
models to perform room modeling and speech recovery. We propose a scheme for
characterizing the room acoustic from the unknown competing speech sources
relying on localization of the early images of the speakers by sparse
approximation of the spatial spectra of the virtual sources in a free-space
model. The images are then clustered exploiting the low-rank structure of the
spectro-temporal components belonging to each source. This enables us to
identify the early support of the room impulse response function and its unique
map to the room geometry. To further tackle the ambiguity of the reflection
ratios, we propose a novel formulation of the reverberation model and estimate
the absorption coefficients through a convex optimization exploiting joint
sparsity model formulated upon spatio-spectral sparsity of concurrent speech
representation. The acoustic parameters are then incorporated for separating
individual speech signals through either structured sparse recovery or inverse
filtering the acoustic channels. The experiments conducted on real data
recordings demonstrate the effectiveness of the proposed approach for
multi-party speech recovery and recognition.Comment: 31 page
Recent Advances in Computational Methods for the Power Flow Equations
The power flow equations are at the core of most of the computations for
designing and operating electric power systems. The power flow equations are a
system of multivariate nonlinear equations which relate the power injections
and voltages in a power system. A plethora of methods have been devised to
solve these equations, starting from Newton-based methods to homotopy
continuation and other optimization-based methods. While many of these methods
often efficiently find a high-voltage, stable solution due to its large basin
of attraction, most of the methods struggle to find low-voltage solutions which
play significant role in certain stability-related computations. While we do
not claim to have exhausted the existing literature on all related methods,
this tutorial paper introduces some of the recent advances in methods for
solving power flow equations to the wider power systems community as well as
bringing attention from the computational mathematics and optimization
communities to the power systems problems. After briefly reviewing some of the
traditional computational methods used to solve the power flow equations, we
focus on three emerging methods: the numerical polynomial homotopy continuation
method, Groebner basis techniques, and moment/sum-of-squares relaxations using
semidefinite programming. In passing, we also emphasize the importance of an
upper bound on the number of solutions of the power flow equations and review
the current status of research in this direction.Comment: 13 pages, 2 figures. Submitted to the Tutorial Session at IEEE 2016
American Control Conferenc
Adaptive text mining: Inferring structure from sequences
Text mining is about inferring structure from sequences representing natural language text, and may be defined as the process of analyzing text to extract information that is useful for particular purposes. Although hand-crafted heuristics are a common practical approach for extracting information from text, a general, and generalizable, approach requires adaptive techniques. This paper studies the way in which the adaptive techniques used in text compression can be applied to text mining. It develops several examples: extraction of hierarchical phrase structures from text, identification of keyphrases in documents, locating proper names and quantities of interest in a piece of text, text categorization, word segmentation, acronym extraction, and structure recognition. We conclude that compression forms a sound unifying principle that allows many text mining problems to be tacked adaptively
On Known-Plaintext Attacks to a Compressed Sensing-based Encryption: A Quantitative Analysis
Despite the linearity of its encoding, compressed sensing may be used to
provide a limited form of data protection when random encoding matrices are
used to produce sets of low-dimensional measurements (ciphertexts). In this
paper we quantify by theoretical means the resistance of the least complex form
of this kind of encoding against known-plaintext attacks. For both standard
compressed sensing with antipodal random matrices and recent multiclass
encryption schemes based on it, we show how the number of candidate encoding
matrices that match a typical plaintext-ciphertext pair is so large that the
search for the true encoding matrix inconclusive. Such results on the practical
ineffectiveness of known-plaintext attacks underlie the fact that even
closely-related signal recovery under encoding matrix uncertainty is doomed to
fail.
Practical attacks are then exemplified by applying compressed sensing with
antipodal random matrices as a multiclass encryption scheme to signals such as
images and electrocardiographic tracks, showing that the extracted information
on the true encoding matrix from a plaintext-ciphertext pair leads to no
significant signal recovery quality increase. This theoretical and empirical
evidence clarifies that, although not perfectly secure, both standard
compressed sensing and multiclass encryption schemes feature a noteworthy level
of security against known-plaintext attacks, therefore increasing its appeal as
a negligible-cost encryption method for resource-limited sensing applications.Comment: IEEE Transactions on Information Forensics and Security, accepted for
publication. Article in pres
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