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Linear Constraints (linear + constraint)

Distribution by Scientific Domains

Mathematics and Statistics	72%
Engineering	18%

Selected Abstracts

NON-SYMMETRICAL CORRESPONDENCE ANALYSIS WITH CONCATENATION AND LINEAR CONSTRAINTS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 1 2010
Eric J. Beh
Summary Correspondence analysis is a popular statistical technique used to identify graphically the presence, and structure, of association between two or more cross-classified categorical variables. Such a procedure is very useful when it is known that there is a symmetric (two-way) relationship between the variables. When such a relationship is known not to exist, non-symmetrical correspondence analysis is more appropriate as a method of establishing the source of association. This paper highlights some tools that can be used to explore the behaviour of asymmetric categorical variables. These tools consist of confidence regions, the link between non-symmetrical correspondence analysis and the analysis of variance of categorical variables, and the effect of imposing linear constraints. We also explore the application of non-symmetrical correspondence analysis to three-way contingency tables. [source]

A FEM,DtN formulation for a non-linear exterior problem in incompressible elasticity

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2003
Gabriel N. Gatica
Abstract In this paper, we combine the usual finite element method with a Dirichlet-to-Neumann (DtN) mapping, derived in terms of an infinite Fourier series, to study the solvability and Galerkin approximations of an exterior transmission problem arising in non-linear incompressible 2d-elasticity. We show that the variational formulation can be written in a Stokes-type mixed form with a linear constraint and a non-linear main operator. Then, we provide the uniqueness of solution for the continuous and discrete formulations, and derive a Cea-type estimate for the associated error. In particular, our error analysis considers the practical case in which the DtN mapping is approximated by the corresponding finite Fourier series. Finally, a reliable a posteriori error estimate, well suited for adaptive computations, is also given. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Reliability Analysis of Technical Systems/Structures by means of Polyhedral Approximation of the Safe/Unsafe Domain

GAMM - MITTEILUNGEN, Issue 2 2007
K. Marti
Abstract Reliability analysis of technical structures and systems is based on an appropriate (limit) state function separating the safe and unsafe/states in the space of random parameters. Starting with the survival conditions, hence, the state equation and the condition for the admissibility of states, an optimizational representation of the state function can be given in terms of the minimum function of a certainminimization problem. Selecting a certain number of boundary points of the safe/unsafe domain, hence, on the limit state surface, the safe/unsafe domain is approximated by a convex polyhedron defined by the intersection of the half spaces in the parameter space generated by the tangent hyperplanes to the safe/unsafe domain at the selected boundary points on the limit state surface. The resulting approximative probability functions are then defined by means of probabilistic linear constraints in the parameter space, where, after an appropriate transformation, the probability distribution of the parameter vector can be assumed to be normal with zero mean vector and unit covariance matrix. Working with separate linear constraints, approximation formulas for the probability of survival of the structure are obtained immediately. More exact approximations are obtained by considering joint probability constraints, which, in a second approximation step, can be evaluated by using probability inequalities and/or discretization of the underlying probability distribution. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A practical approach for estimating illumination distribution from shadows using a single image

INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 2 2005
Taeone Kim
Abstract This article presents a practical method that estimates illumination distribution from shadows using only a single image. The shadows are assumed to be cast on a textured, Lambertian surface by an object of known shape. Previous methods for illumination estimation from shadows usually require that the reflectance property of the surface on which shadows are cast be constant or uniform, or need an additional image to cancel out the effects of varying albedo of the textured surface on illumination estimation. But, our method deals with an estimation problem for which surface albedo information is not available. In this case, the estimation problem corresponds to an underdetermined one. We show that the combination of regularization by correlation and some user-specified information can be a practical method for solving the underdetermined problem. In addition, as an optimization tool for solving the problem, we develop a constrained Non-Negative Quadratic Programming (NNQP) technique into which not only regularization but also multiple linear constraints induced by user-specified information are easily incorporated. We test and validate our method on both synthetic and real images and present some experimental results. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 15, 143,154, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20047 [source]

Modeling and optimization of cylindrical antennas using the mode-expansion method and genetic algorithms

INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 6 2005
Dawei Shen
Abstract For monopole antennas with cylindrically symmetric structures, a mode-expansion method is highly time efficient, which is a realistic approach for integrating function-optimization tools, such as genetic algorithms (GAs), in order to extract the best bandwidth property. In this article, a mode-expansion method is used to simulate the impedance characteristics of the cylindrical antennas. As examples, two new types of monopole antennas are presented, one of which possesses a two-step top-hat structure while the other has an annulus around the stem. After the modeling scheme is examined for convergence and data validity, the associated optimization problem, with dimensions as decision variables, structural limitations as linear constraints, and desired bandwidth performance as an objective function, is solved using GAs. The effects of the geometric parameters on the impedance characteristics are investigated in order to demonstrate the optimality of the calculated solutions. Two optimized practical antennas are designed based on our numerical studies. One has a broad bandwidth of 3 GHz while the other shows a dual-band property, which can satisfy the bandwidth requirements for both Bluetooth (2.45-GHz band) and WLAN (5-GHz band) systems. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2005. [source]

Constrained Kalman Filtering: Additional Results

INTERNATIONAL STATISTICAL REVIEW, Issue 2 2010
Adrian Pizzinga
Summary This paper deals with linear state space modelling subject to general linear constraints on the state vector. The discussion concentrates on four topics: the constrained Kalman filtering versus the recursive restricted least squares estimator; a new proof of the constrained Kalman filtering under a conditional expectation framework; linear constraints under a reduced state space modelling; and state vector prediction under linear constraints. The techniques proposed are illustrated in two real problems. The first problem is related to investment analysis under a dynamic factor model, whereas the second is about making constrained predictions within a GDP benchmarking estimation. Résumé Cet article traite des modèles espace-état sujets aux restrictions linéaires générales sur le vecteur d'état. La discussion se concentre autour de quatre aspects: le filtrage de Kalman restreint versus l'estimateur de moindres carrés restreint recursive; une nouvelle preuve du filtrage de Kalman restreint sous le cadre de l'espérance conditionelle; restrictions linéaires aux modèles espace-état réduits; et la prédiction d'état sous restrictions linéaires. Les techniques proposées sont illustrées par deux problèmes réels. Le premier problème est concerné par l'analyse d'investissement sous un modèle à facteur dynamique, tandis que le second concerne les prédictions restreintes dans l'estimation de benchmarking. [source]

A spatial queuing approach to optimize coordinated signal settings to obviate gridlock in adjacent work zones

JOURNAL OF ADVANCED TRANSPORTATION, Issue 4 2010
C.K. Wong
Abstract Gridlock is defined when traffic comes to a complete halt inducing huge delays. If a work zone on a two-lane two-way highway is set up, in which one of the traffic lanes is closed for maintenance road works, the remaining lane has to be controlled to serve the two-way traffic alternatively. The study objective is to optimize the traffic signal controls across two closely spaced work zones to prevent a gridlock, which can occur easily if upstream and downstream signals are not well coordinated. When vehicle queues build up in the middle sections between two work zones and further expand to occupy the single available lanes in both directions, the two-way traffic is then blocked and no vehicle can leave from the queues generating a gridlock. To address this problem, spatial queues are important parameters that must be explicitly analyzed. The cell transmission model, which is known to be a robust mathematical tool for the modeling of queue dynamics, is adopted in this study. A signal cell is used to represent each traffic signal control, the exit flow capacity of which is defined in accordance with the signal plan. A set of linear constraints is established to relate all of the model parameters and variables. The objective function is taken as the total number of vehicles in the critical section between the two work zones. The minimization of this objective function can effectively obviate the occurrence of a gridlock. The optimization problem is formulated as a Binary-Mixed-Integer-Linear-Program that can be solved by the standard branch-and-bound technique. Numerical examples are given to demonstrate the effectiveness of the proposed methodology. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Generalized linear models incorporating population level information: an empirical-likelihood-based approach

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2008
Sanjay Chaudhuri
Summary., In many situations information from a sample of individuals can be supplemented by population level information on the relationship between a dependent variable and explanatory variables. Inclusion of the population level information can reduce bias and increase the efficiency of the parameter estimates. Population level information can be incorporated via constraints on functions of the model parameters. In general the constraints are non-linear, making the task of maximum likelihood estimation more difficult. We develop an alternative approach exploiting the notion of an empirical likelihood. It is shown that, within the framework of generalized linear models, the population level information corresponds to linear constraints, which are comparatively easy to handle. We provide a two-step algorithm that produces parameter estimates by using only unconstrained estimation. We also provide computable expressions for the standard errors. We give an application to demographic hazard modelling by combining panel survey data with birth registration data to estimate annual birth probabilities by parity. [source]

Generating Pareto-optimal boundary points in multiparty negotiations using constraint proposal method

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2001
Pirja Heiskanen
Abstract In this paper a constraint proposal method is developed for computing Pareto-optimal solutions in multiparty negotiations over continuous issues. Constraint proposal methods have been previously studied in a case where the decision set is unconstrained. Here we extend the method to situations with a constrained decision set. In the method the computation of the Pareto-optimal solutions is decentralized so that the DMs do not have to know each others' value functions. During the procedure they have to indicate their optimal solutions on different sets of linear constraints. When the optimal solutions coincide, the common optimum is a candidate for a Pareto-optimal point. The constraint proposal method can be used to generate either one Pareto-optimal solution dominating the status quo solution or several Pareto-optimal solutions. In latter case a distributive negotiation among the efficient points can be carried out afterwards. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 210,225, 2001 [source]