Stability analysis of an aperiodic sampled-data control system is considered for application to network and embedded control. The stability condition is described in a linear matrix inequality to be satisfied for all ...
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Stability analysis of an aperiodic sampled-data control system is considered for application to network and embedded control. The stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals. Although this condition is numerically intractable,a tractable sufficient condition can be constructed with the mean value theorem. Special attention is paid to tightness of the sufficient condition for less conservative stability analysis.A region-dividing technique for reduction of conservatism and generalization to stabilization are also discussed. Examples show the efficacy of the approach.
semidefinite programs are convex optimization problems arising in a wide variety of applications and are the extension of linear programming. Most methods for linear programming have been generalized to semidefinite p...
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semidefinite programs are convex optimization problems arising in a wide variety of applications and are the extension of linear programming. Most methods for linear programming have been generalized to semidefinite programs. Just as in linear programming, duality theorem plays a basic and an important role in theory as well as in algorithmics. Based on the discretization method and convergence property, this paper proposes a new proof of the strong duality theorem for semidefinite programming, which is different from other common proofs and is more simple. (C) 2004 Elsevier Inc. All rights reserved.
We propose a class of semidefinite programming (SDP) problems for which an optimal solution can be calculated directly, i.e., without using an iterative method. Several classes of such SDP problems have been proposed....
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We propose a class of semidefinite programming (SDP) problems for which an optimal solution can be calculated directly, i.e., without using an iterative method. Several classes of such SDP problems have been proposed. Among them, Vanderbei and Yang (1995), Ohara (1998), and Wolkovicz (1996) are well known. We show that our class contains all of the three classes as special cases.
In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polyno...
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ISBN:
(纸本)354024297X
In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polynomial form. Then the unknown rank function and invariants are abstracted in parametric form. The implication in the Floyd/Naur/Hoare verification conditions is handled by abstraction into numerical constraints by Lagrangian relaxation. The remaining universal quantification is handled by semidefinite programming relaxation. Finally the parameters are computed using semidefinite programming solvers. This new approach exploits the recent progress in the numerical resolution of linear or bilinear matrix inequalities by semidefinite programming using efficient polynomial primal/dual interior point methods generalizing those well-known in linear programming to convex optimization. The framework is applied to invariance and termination proof of sequential, nondeterministic, concurrent, and fair parallel imperative polynomial programs and can easily be extended to other safety and liveness properties.
We consider the problem min(X epsilon(0, 1)n) {c'x : a'(j)x <= b(j), j = 1,..., m), where the a(j) are random vectors with unknown distributions. The only information we are given regarding the random vecto...
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We consider the problem min(X epsilon(0, 1)n) {c'x : a'(j)x <= b(j), j = 1,..., m), where the a(j) are random vectors with unknown distributions. The only information we are given regarding the random vectors aj are their moments, up to order k. We give a robust formulation, as a function of k, for the 0-1 integer linear program under this limited distributional information. (C) 2007 Elsevier B.V. All rights reserved.
Regularized kernel discriminant analysis (RKDA) performs linear discriminant analysis in the feature space via the kernel trick. Its performance depends on the selection of kernels. In this paper, we consider the prob...
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Regularized kernel discriminant analysis (RKDA) performs linear discriminant analysis in the feature space via the kernel trick. Its performance depends on the selection of kernels. In this paper, we consider the problem of multiple kernel learning (MKL) for RKDA, in which the optimal kernel matrix is obtained as a linear combination of pre-specified kernel matrices. We show that the kernel learning problem in RKDA can be formulated as convex programs. First, we show that this problem can be formulated as a semidefinite program (SDP). Based on the equivalence relationship between RKDA and least square problems in the binary-class case, we propose a convex quadratically constrained quadratic programming (QCQP) formulation for kernel learning in RKDA. A semi-infinite linear programming (SILP) formulation is derived to further improve the efficiency. We extend these formulations to the multi-class case based on a key result established in this paper. That is, the multi-class RKDA kernel learning problem can be decomposed into a set of binary-class kernel learning problems which are constrained to share a common kernel. Based on this decomposition property, SDP formulations are proposed for the multi-class case. Furthermore, it leads naturally to QCQP and SILP formulations. As the performance of RKDA depends on the regularization parameter, we show that this parameter can also be optimized in a joint framework with the kernel. Extensive experiments have been conducted and analyzed, and connections to other algorithms are discussed.
This is a summary of the author's PhD thesis supervised by A. Billionnet and S. Elloumi and defended on November 2006 at the CNAM, Paris (Conservatoire National des Arts et Metiers). The thesis is written in Frenc...
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This is a summary of the author's PhD thesis supervised by A. Billionnet and S. Elloumi and defended on November 2006 at the CNAM, Paris (Conservatoire National des Arts et Metiers). The thesis is written in French and is available from http://***/PUBLIS/RC1115. This work deals with exact solution methods based on reformulations for quadratic 0-1 programs under linear constraints. These problems are generally not convex;more precisely, the associated continuous relaxation is not a convex problem. We developed approaches with the aim of making the initial problem convex and of obtaining a good lower bound by continuous relaxation. The main contribution is a general method (called QCR) that we implemented and applied to classical combinatorial optimization problems.
The track-to-track association problem is to determine the pairing of sensor-level tracks that correspond to the same true target from which the sensor-level tracks originated. This problem is crucial for multisensor ...
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ISBN:
(纸本)9780982443804
The track-to-track association problem is to determine the pairing of sensor-level tracks that correspond to the same true target from which the sensor-level tracks originated. This problem is crucial for multisensor data fusion and is complicated by the presence of individual sensor biases, random errors, false tracks, and missed tracks. A popular approach to performing track-to-track association between two sensor systems is to jointly optimize the a posteriori relative bias estimate between the sensors and the likelihood of track-to-track association. Algorithms that solve this problem typically generate the K best bias-association hypotheses and corresponding bias-association likelihoods. In this paper, we extend the above approach in two ways. First, we derive a closed-form expression for computing "pure" track-to-track association likelihoods, as opposed to bias-association likelihoods which are weighted by a unique relative bias estimate. Second, we present an alternative formulation of the track-to-track association problem in which we optimize solely with respect to association likelihoods. These results facilitate what is commonly known as system-level track ambiguity management.
We consider the problem of finding a low-rank approximate solution to a system of linear equations in symmetric, positive semidefinite matrices, where the approximation quality of a solution is measured by its maximum...
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We consider the problem of finding a low-rank approximate solution to a system of linear equations in symmetric, positive semidefinite matrices, where the approximation quality of a solution is measured by its maximum relative deviation, both above and below, from the prescribed quantities. We show that a simple randomized polynomial-time procedure produces a low-rank solution that has provably good approximation qualities. Our result provides a unified treatment of and generalizes several well-known results in the literature. In particular, it contains as special cases the Johnson-Lindenstrauss lemma on dimensionality reduction, results on low-distortion embeddings into low-dimensional Euclidean space, and approximation results on certain quadratic optimization problems.
In this paper, we investigate two soft-biometric problems: 1) age estimation and 2) pose estimation, within the scenario where uncertainties exist for the available labels of the training samples. These two tasks are ...
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In this paper, we investigate two soft-biometric problems: 1) age estimation and 2) pose estimation, within the scenario where uncertainties exist for the available labels of the training samples. These two tasks are generally formulated as the automatic design of a regressor from training samples with uncertain nonnegative labels. First, the nonnegative label is predicted as the Frobenius norm of a matrix, which is bilinearly transformed from the nonlinear mappings of a set of candidate kernels. Two transformation matrices are then learned for deriving such a matrix by solving two semidefinite programming (SDP) problems, in which the uncertain label of each sample is expressed as two inequality constraints. The objective function of SDP controls the ranks of these two matrices and, consequently, automatically determines the structure of the regressor. The whole framework for the automatic design of a regressor from samples with uncertain nonnegative labels has the following characteristics: 1) the SDP formulation makes full use of the uncertain labels, instead of using conventional fixed labels;2) regression with the Frobenius norm of matrix naturally guarantees the nonnegativity of the labels, and greater prediction capability is achieved by integrating the squares of the matrix elements, which to some extent act as weak regressors;and 3) the regressor structure is automatically determined by the pursuit of simplicity, which potentially promotes the algorithmic generalization capability. Extensive experiments on two human age databases: 1) FG-NIET and 2) Yamaha, and the Pointing'04 head pose database, demonstrate encouraging estimation accuracy improvements over conventional regression algorithms without taking the uncertainties within the labels into account.
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