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13
A proximal method for composite minimization
, 2008
"... Abstract. We consider minimization of functions that are compositions of proxregular functions with smooth vector functions. A wide variety of important optimization problems can be formulated in this way. We describe a subproblem constructed from a linearized approximation to the objective and a r ..."
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Cited by 15 (3 self)
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Abstract. We consider minimization of functions that are compositions of proxregular functions with smooth vector functions. A wide variety of important optimization problems can be formulated in this way. We describe a subproblem constructed from a linearized approximation to the objective and a regularization term, investigating the properties of local solutions of this subproblem and showing that they eventually identify a manifold containing the solution of the original problem. We propose an algorithmic framework based on this subproblem and prove a global convergence result.
Inference of complex biological networks: distinguishability issues and optimizationbased solutions
 BMC Systems Biology
"... Background: The inference of biological networks from highthroughput data has received huge attention during the last decade and can be considered an important problem class in systems biology. However, it has been recognized that reliable network inference remains an unsolved problem. Most authors ..."
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Background: The inference of biological networks from highthroughput data has received huge attention during the last decade and can be considered an important problem class in systems biology. However, it has been recognized that reliable network inference remains an unsolved problem. Most authors have identified lack of data and deficiencies in the inference algorithms as the main reasons for this situation. Results: We claim that another major difficulty for solving these inference problems is the frequent lack of uniqueness of many of these networks, especially when prior assumptions have not been taken properly into account. Our contributions aid the distinguishability analysis of chemical reaction network (CRN) models with mass action dynamics. The novel methods are based on linear programming (LP) , therefore they allow the efficient analysis of CRNs containing several hundred complexes and reactions. Using these new tools and also previously published ones to obtain the network structure of biological systems from the literature, we find that, often, a unique topology cannot be determined, even if the structure of the corresponding mathematical model is assumed to be known and all dynamical variables are measurable. In other words, certain mechanisms may remain undetected (or they are falsely detected) while the inferred model is fully consistent with the measured data. It is also shown that sparsity enforcing approaches for determining ‘true ’ reaction structures are
Sparse representation of solutions of Kronecker product systems
, 2008
"... Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. Fo ..."
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Cited by 6 (0 self)
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Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. For the mutual incoherence we also discuss results for sums of Kronecker products.
Efficient Computations of a Security Index for False Data Attacks in Power Networks
, 2013
"... The resilience of Supervisory Control and Data ..."
Compressive sensing: a paradigm shift in signal processing
, 2008
"... We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the ShannonNyquist sampling principle, the new theory shows that it is possible to reconstruct images or signals of scientific interest a ..."
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Cited by 1 (0 self)
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We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the ShannonNyquist sampling principle, the new theory shows that it is possible to reconstruct images or signals of scientific interest accurately and even exactly from a number of samples which is far smaller than the desired resolution of the image/signal, e.g., the number of pixels in the image. This new technique draws from results in several fields of mathematics, including algebra, optimization, probability theory, and harmonic analysis. We will discuss some of the key mathematical ideas behind compressive sensing, as well as its implications to other fields: numerical analysis, information theory, theoretical computer science, and engineering.
Sparse Approximate Solution of Partial Differential Equations
, 2008
"... A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure is presented that uses linear programming to find a good app ..."
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A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure is presented that uses linear programming to find a good approximation to the sparse solution on a given refinement level. Then only those parts of the mesh are refined that belong to nonzero expansion coefficients. Error estimates for this procedure are refined and the behavior of the procedure is demonstrated via some simple elliptic model problems.
GT200959099 A SPARSE ESTIMATION APPROACH TO FAULT ISOLATION
"... ABSTRACT Leastsquaresbased methods are very popular in the jet engine community for health monitoring purpose. In most practical situations, the number of health parameters exceeds the number of measurements, making the estimation problem underdetermined. To address this issue, regularisation add ..."
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ABSTRACT Leastsquaresbased methods are very popular in the jet engine community for health monitoring purpose. In most practical situations, the number of health parameters exceeds the number of measurements, making the estimation problem underdetermined. To address this issue, regularisation adds a penalty term on the deviations of the health parameters. Generally, this term imposes a quadratic penalisation on these deviations. A sideeffect of this technique is a relatively poor isolation capability. The latter feature can be improved by recognizing that abrupt faults impact at most one or two component(s) simultaneously. This translates mathematically into the search for a sparse solution. The present contribution reports the development of a fault isolation tool favouring sparse solutions. It is very efficiently implemented in the form of a quadratic program. As a validation procedure, the resulting algorithm is applied to a variety of fault conditions simulated with a generic commercial turbofan model.
METHODOLOGY ARTICLE Open Access
"... Inference of complex biological networks: distinguishability issues and optimizationbased solutions ..."
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Inference of complex biological networks: distinguishability issues and optimizationbased solutions
Recent Advances in Mathematical Programming with Semicontinuous Variables and Cardinality Constraint
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Integrated Classifier Hyperplane Placement and Feature Selection
, 2011
"... Errata are shown in red. The process of placing a separating hyperplane for data classification is normally disconnected from the process of selecting the features to use. An approach for feature selection that is conceptually simple but computationally explosive is to simply apply the hyperplane pl ..."
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Errata are shown in red. The process of placing a separating hyperplane for data classification is normally disconnected from the process of selecting the features to use. An approach for feature selection that is conceptually simple but computationally explosive is to simply apply the hyperplane placement process to all possible subsets of features, selecting the smallest set of features that provides reasonable classification accuracy. Two ways to speed this process are (i) use a faster filtering criterion instead of a complete hyperplane placement, and (ii) use a greedy forward or backwards sequential selection method. This paper introduces a new filtering criterion that is very fast: maximizing the drop in the sum of infeasibilities in a linearprogramming transformation of the problem. It also shows how the linear programming transformation can be applied to reduce the number of features after a separating hyperplane has already been placed while maintaining the separation that was originally induced by the hyperplane. Finally, a new and highly effective integrated method that simultaneously selects features while placing the separating hyperplane is introduced. 1.