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Dissertations / Theses on the topic 'Lagrangian functions'
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Brown, Jeffrey W. "Lagrangian field observations of rip currents." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 133 p, 2008. http://proquest.umi.com/pqdweb?did=1633772921&sid=6&Fmt=2&clientId=8331&RQT=309&VName=PQD.
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Lai, Shih-yih. "Lagrangian relaxation and discrete optimization problems /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.
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Hare, Warren L. "The Quadratic Sub-Lagrangian of prox-regular functions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ60128.pdf.
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Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.
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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.Committee Chair: Gangbo, Wilfrid; Committee Member: Chow, Shui-Nee; Committee Member: Harrell, Evans; Committee Member: Swiech, Andrzej; Committee Member: Yezzi, Anthony Joseph. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Zhou, Long. "Mesoscale variability and Lagrangian statistics in the tropical North Atlantic /." View online ; access limited to URI, 2009. http://digitalcommons.uri.edu/dissertations/AAI3401129.
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Uygun, Adnan. "Network interdiction by Lagrangian relaxation and branch-and-bound." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2002. http://library.nps.navy.mil/uhtbin/hyperion-image/02Jun%5FUygun.pdf.
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Song, Qiang. "Non-euler-lagrangian pareto-optimality conditions for dynamic multiple-criterion decision problems." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/24920.
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Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.
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In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is revealed to be a powerful tool for proving convergence of our algorithm. Finally, we analyze uniqueness and stability of our solution in L¹.
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Silverberg, Jon P. "On Lagrangian meshless methods in free-surface flows." Thesis, (1.7 MB), 2005. http://edocs.nps.edu/AR/topic/theses/2005/Jan/05Jan_Silverberg.pdf.
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Thesis (Master of Engineering in Ocean Engineering)--University of California at Berkeley, 2004."January 2005." Description based on title screen as viewed on May 25, 2010. DTIC Descriptor(s): Fluid Dynamics, Lagrangian Functions, Equations Of Motion, Acceleration, Formulations, Grids, Continuum Mechanics, Gaussian Quadrature, Derivatives (Mathematics), Compact Disks, Boundary Value Problems, Polynomials, Interpolation, Pressure, Operators (Mathematics). DTIC Identifier(s): Multimedia (CD-Rom), Moving Grids, Meshless Discretization, Lifs (Lagrange Implicit Fraction Step), Lagrangian Dynamics, Meshless Operators, Mlip (Multidimensional Lagrange Interpolating Polynomials), Flux Boundary Conditions, Radial Basis Functions Includes bibliographical references (58-59).
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Almesallmy, Mohammed. "Experimental and analytical investigation of inertial propulsion mechanisms and motion simulation of rigid-multi-body mechanical systems /." View online ; access limited to URI, 2006. http://0-digitalcommons.uri.edu.helin.uri.edu/dissertations/3239899.
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Lee, Chun Hean. "Development of a cell centred upwind finite volume algorithm for a new conservation law formulation in structural dynamics." Thesis, Swansea University, 2012. https://cronfa.swan.ac.uk/Record/cronfa42726.
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Over the past few decades, dynamic solid mechanics has become a major field of interest in industrial applications involving crash simulation, impact problems, forging and many others to be named. These problems are typically nonlinear due to large deformations (or geometrical nonlinearity) and nonlinear constitutive relations (or material nonlinearity). For this reason, computer simulations for such problems are of practical importance. In these simulations, the Lagrangian formulation is typically used as it automatically satisfies the mass conservation law. Explicit numerical methods are considered to be efficient in these cases. Most of the numerical methods employed for such simulations are developed from the equation of motion (or momentum balance principle). The use of low-order elements in these numerical methods often exhibits the detrimental locking phenomena in the analysis of nearly incompressible applications, which produces an undesirable effect leading to inaccurate results. Situations of this type are usual in the solid dynamics analysis for rubber materials and metal forming processes. In metal plasticity, the plastic deformation is isochoric (or volume-preserving) whereas, the compressible part is due only to elastic deformation. Recently, a new mixed formulation has been established for explicit Lagrangian transient solid dynamics. This formulation, involving linear momentum, deformation gradient and total energy, results in first order hyperbolic system of equations. Such conservation-law formulation enables stresses to converge at the same rate as velocities and displacements. In addition, it ensures that low order elements can be used without volumetric locking and/or bending difficulty for nearly incompressible applications. The new mixed formulation itself shows a clear advantage over the classical displacement-based formulation, due to its simplicity in incorporating state-of-the-art shock capturing techniques. In this research, a curl-preserving cell centred finite volume computational methodology is presented for solving the first order hyperbolic system of conservation laws on quadrilateral cartesian grids. First, by assuming that the approximation to the unknown variables is constant within each cell. This will lead to discontinuities at cell edges which will motivate the use of a Riemann solver by introducing an upwind bias into the evaluation of the numerical flux function. Unfortunately, the accuracy is severely undermined by an excess of numerical dissipation. In order to alleviate this, it is vital to introduce a linear reconstruction procedure for enhancing the accuracy of the scheme. However the second-order spatial method does not prohibit spurious oscillation in the vicinity of sharp gradients. To circumvent this, a nonlinear slope limiter will then be introduced. It is now possible to evolve the semi-discrete evolutionary system of ordinary equations in time with the aid of the family of explicit Total Variation Diminishing Runge Kutta (TVD-RK) time marching schemes. Moreover, a correction procedure involving minimisation algorithm for conservation of the total angular momentum is presented. To this end, a number of interesting examples will be examined in order to demonstrate the robustness and general capabilities of the proposed approach.
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Choi, Gyunghyun. "Nondifferentiable optimization algorithms with application to solving Lagrangian dual problems." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/38657.
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Hall, Bryan, University of Western Sydney, and of Science Technology and Environment College. "Energy and momentum conservation in Bohm's Model for quantum mechanics." THESIS_CSTE_XXX_Hall_B.xml, 2004. http://handle.uws.edu.au:8081/1959.7/717.
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Bohm's model for quantum mechanics is examined and a well-known drawback of the model is considered, namely the fact that the model does not conserve energy and momentum.It is shown that the Lagrangian formalism and the use of energy-momentum tensors provide a way of addressing this non-conservation aspect once the model is considered from the point of view of an interacting particle-field system. The full mathematical formulation that is then presented demonstrates that conservation can be reintroduced without disrupting the present agreement of Bohm's model with experiment.Doctor of Philosphy (PhD)
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Morales-Silva, Daniel. "G-coupling functions and properties of strongly star-shaped cones." Thesis, University of Ballarat, 2009. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/34661.
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The main part of this thesis presents a new approach to the topic of conjugation, with applications to various optimization problems. It does so by introducing (what we call) G-coupling functions.Doctor of Philosophy
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Hall, Bryan. "Energy and momentum conservation in Bohm's Model for quantum mechanics." Thesis, View thesis, 2004. http://handle.uws.edu.au:8081/1959.7/717.
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Bohm's model for quantum mechanics is examined and a well-known drawback of the model is considered, namely the fact that the model does not conserve energy and momentum.It is shown that the Lagrangian formalism and the use of energy-momentum tensors provide a way of addressing this non-conservation aspect once the model is considered from the point of view of an interacting particle-field system. The full mathematical formulation that is then presented demonstrates that conservation can be reintroduced without disrupting the present agreement of Bohm's model with experiment.
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Leijon, Rasmus. "On the geometry of calibrated manifolds : with applications to electrodynamics." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80675.
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In this master thesis we study calibrated geometries, a family of Riemannian or Hermitian manifolds with an associated differential form, φ. We show that it isuseful to introduce the concept of proper calibrated manifolds, which are in asense calibrated manifolds where the geometry is derived from the calibration. In particular, the φ-Grassmannian is considered in the case of proper calibratedmanifolds. The impact of proper calibrated manifolds as a model is studied, aswell as the usefulness of pluripotential theory as tools for the model. The specialLagrangian calibration is an example of an important calibration introduced byHarvey and Lawson, which leads to the definition of the special Lagrangian differentialequation. This partial differential equation can be formulated in threeand four dimensions as det(H(u)) = Δu, where H(u) is the Hessian matrix of some potential u. We prove the existence of solutions and some other propertiesof this nonlinear differential equation and present the resulting 6- and 8-dimensional manifolds defined by the graph {x + i
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Sun, Xiaoqing. "A modified shifting bottleneck approach to job shop scheduling with sequence dependent setups (MSBSS) /." free to MU campus, to others for purchase, 1997. http://wwwlib.umi.com/cr/mo/fullcit?p9841187.
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Chen, Hong. "Mechanisms and modelling of landslides in Hong Kong /." Hong Kong : University of Hong Kong, 1999. http://sunzi.lib.hku.hk/hkuto/record.jsp?B21375513.
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Hall, Bryan. "Energy and momentum conservation in Bohm's Model for quantum mechanics." View thesis, 2004. http://library.uws.edu.au/adt-NUWS/public/adt-NUWS20040507.155043/index.html.
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Devkota, Bishnu Hari. "A new Lagrangian model for the dynamics and transport of river and shallow water flows." University of Western Australia. Centre for Water Research, 2005. http://theses.library.uwa.edu.au/adt-WU2005.0108.
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This study presents a new Lagrangian model for predicting dynamics and transport in rivers and shallow water flows. A hydrostatic model is developed for the prediction of rivers and floodplain flow and lateral interactions between them. The model is extended to the Boussinesq weakly non-linear, non-hydrostatic model for the simulation of solitary waves and undular bores. A model for advection-diffusion transport of tracers in open channel flow is also presented. The simulation results are compared against an analytical solution and published laboratory data, field data and theoretical results. It is demonstrated that the Lagrangian moving grid eliminates numerical diffusion and oscillations; the model is dynamically adaptive, providing higher resolution under the wave by compressing the parcels (grid). It also allows flow over dry beds and moving boundaries to be handled efficiently. The hydrostatic model results have shown that the model accurately simulates wave propagation and non-linear steepening until wave breaking. The model is successfully applied to simulate flow and lateral interactions in a compound channel and flood wave movement in a natural river. The non-hydrostatic model has successfully reproduced the general features of solitary waves such as the balance between non-linearity and wave dispersion and non-linear interactions of two solitary waves by phase-shift. Also, the model successfully reproduced undular bores (high frequency short waves) from a long wave and the predicted maximum height of the leading wave agreed very well with the published results. It is shown that the simple second order accurate Lagrangian scheme efficiently simulates dispersive waves without any numerical diffusion. Lagrangian modeling of advection-diffusion transport of Gaussian tracer distributions, top hat tracer distributions and steep fronts (step function) in steady, uniform flow has provided exact results and has shown that the scheme allows the use of a large time step without any numerical diffusion and oscillations, including for the advection of steep fronts. The scheme can handle large Courant numbers (results are presented for Cr = 0 to 20) and the entire range of grid Peclet numbers from zero to infinity. The model is successfully applied to tracer transport due to flow induced by simple waves, solitary waves and undular bores
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Huang, Lingyan. "Mass transport due to surface waves in a water-mud system." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B35380457.
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Huang, Lingyan, and 黃凌燕. "Mass transport due to surface waves in a water-mud system." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B35380457.
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Dewasurendra, Lohitha. "A finite element method for ring rolling processes." Ohio : Ohio University, 1998. http://www.ohiolink.edu/etd/view.cgi?ohiou1175098096.
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Lambert, Alex. "Learning function-valued functions in reproducible kernel Hilbert spaces with integral losses : Application to infinite task learning." Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAT016.
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Les méthodes à noyaux sont au coeur de l'apprentissage statistique. Elles permettent de modéliser des fonctions à valeurs réelles dans des espaces de fonctions à fort potentiel représentatif, sur lesquels la minimisation de risques empiriques régularisés est possible et produit des estimateurs dont le comportement statistique est largement étudié. Lorsque les sorties ne sont plus réelles mais de plus grande dimension, les Espaces de Hilbert à Noyaux Reproduisants à valeurs vectorielles (vv-RKHSs) basés sur des Noyaux à Valeurs Opérateurs (OVKs) fournissent des espaces de fonctions similaires et permettent de traiter des problèmes tels que l'apprentissage multi-tâche, la prédiction structurée ou la régression à valeurs fonctionnelles. Dans cette thèse, nous introduisons une extension fonctionnelle originale du cadre multi-tâche appelée Apprentissage d'un Continuum de Tâches (ITL), qui permet de résoudre conjointement un continuum de tâches paramétrées, parmi lesquelles la régression quantile, la classification à coût assymétrique, ou l'estimation de niveaux de densité. Nous proposons un cadre d'apprentissage basé sur des fonctions de pertes intégrales qui comprend à la fois l'ITL et la régression à valeurs fonctionnelles, ainsi que des méthodes d'optimisation pour résoudre les problèmes de minimisation de risque empirique régularisé résultants. Par un échantillonage des pertes intégrales, nous obtenons une représentation de dimension finie des solutions pour différents choix de régularisation ou pénalités liées à la forme des fonctions, tout en gardant un contrôle théorique sur les capacités en généralisation des estimateurs. L'usage de la dualité lagrangienne vient approfondir ces méthodes, en apportant en particulier les moyens d'imposer des estimateurs parcimonieux ou robustes à l'aide de pertes convoluées. Les problèmes de passages à l'échelle sont traités par l'utilisation noyaux approchés, dont les vv-RKHSs associés sont de dimension finie. Nous proposons aussi une architecture composée d'un réseau de neurone et d'une dernière couche à noyaux, qui permet l'apprentissage de représentations appropriées aux noyaux utiles dans les applications avec des données complexes comme les images. Ces techniques sont appliquées à plusieurs problèmes d'ITL, ainsi qu'au problème de régression fonction-à-fonction robuste en présence de valeurs aberrantes. Enfin, nous revisitons les problemes de transfert de style sous l'angle ITL, avec une application au transfert d'émotionKernel methods are regarded as a cornerstone of machine learning.They allow to model real-valued functions in expressive functional spaces, over which regularized empirical risk minimization problems are amenable to optimization and yield estimators whose statistical behavior is well studied. When the outputs are not reals but higher dimensional, vector-valued Reproducible Kernel Hilbert Spaces (vv-RKHSs) based on Operator-Valued Kernels (OVKs) provide similarly powerful spaces of functions, and have proven useful to tackle problems such as multi-task learning, structured prediction, or function-valued regression.In this thesis, we introduce an original functional extension of multi-output learning called Infinite Task Learning (ITL), that allows to jointly solve an infinite number of parameterized tasks, including for instance quantile regression, cost-sensitive classification and density level set estimation.We propose a learning framework based on convex integral losses that encompasses the ITL problem and function-valued regression. Optimization schemes dedicated to solving the associated regularized empirical risk minimization problems are designed. By sampling the integral losses, we derive finite-dimensional representation of the solution under several choices of regularizers or shape constraints penalties, while keeping theoretical guarantees over their generalization capabilities. We also employ dualization techniques with the benefit of bringing desirable properties such as robustness or sparsity to the estimators thanks to the use of convoluted losses. Scalability issues are addressed by deriving optimization algorithms in the the context of approximated OVKs whose corresponding vv-RKHSs are of finite dimension. The use of trainable deep architectures composed by a neural network followed by a shallow kernel layer is also investigated as a way to learn the kernel used in practice on complex data such as images.We apply these techniques to various ITL problems and to robust function-to-function regression, that are tackled in the presence of outliers. We also cast style transfer problems as a vectorial output ITL problem and demonstrate its efficiency in emotion transfer
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Stay, Justin L. "Multi-beam-interference-based methodology for the fabrication of photonic crystal structures." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31783.
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Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2010.Committee Chair: Thomas K. Gaylord; Committee Member: Donald D. Davis; Committee Member: Gee-Kung Chang; Committee Member: Muhannad S. Bakir; Committee Member: Phillip N. First. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Chen, Hong, and 陳虹. "Mechanisms and modelling of landslides in Hong Kong." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31239948.
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Goncalves, Juliana Bittencourt. "EMPREGO DE UM MODELO DE DISPERSÃO TURBULENTO NO ESTUDO DA UNIVERSALIDADE DA TAXA DE DISSIPAÇÃO DA ENERGIA." Universidade Federal de Santa Maria, 2010. http://repositorio.ufsm.br/handle/1/10254.
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Conselho Nacional de Desenvolvimento Científico e TecnológicoThis study employed different autocorrelation functions and Maclaurin series expansions in the derivation of expressions describing the dissipation rate of turbulent kinetic energy. These expressions have the same functional form, but are described in terms of different numerical coefficients. The values obtained for the numerical coefficients were used in a Lagrangian stochastic dispersion model to simulate the dispersion of contaminants in the Planetary Boundary Layer (PBL). The simulation results were compared with concentration data observed in the Copenhagen experiment. The good performance of the parameterization and analysis through statistical indices showed that the mathematical relationships that describe the turbulent dissipation rate present an uncertainty. The analysis developed in this study indicates that there is no a universal functional form describing the dissipation rate of turbulent energy.
Neste estudo foram empregadas diferentes funções de autocorrelação e expansões em série de Maclaurin na derivação de expressões que descrevem a taxa de dissipação da energia cinética turbulenta. Estas expressões apresentam a mesma forma funcional, porém são descritas em termos de diferentes coeficientes numéricos. Os valores obtidos para os coeficientes numéricos foram empregados em um modelo de dispersão estocástico Lagrangiano para simular a dispersão de contaminantes na Camada Limite Planetária (CLP). Os resultados das simulações foram comparados com dados de concentração do experimento de Copenhagen. O bom desempenho da parametrização e a análise através de índices estatísticos permitiram concluir que as relações matemáticas que descrevem a taxa de dissipação da turbulenta, apresentam uma incerteza. A análise desenvolvida nesse estudo permite concluir que não existe uma forma funcional universal descrevendo a taxa de dissipação de energia turbulenta.
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Flores, Callisaya Hector 1980. "Empacotamento em quadráticas." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307468.
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Orientador: José Mario Martínez PérezTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Neste trabalho, serão propostos modelos matemáticos para problemas de empacotamento não reticulado de esferas em regiões limitadas por quadráticas no plano e no espaço. Uma técnica para construir representações ou parametrizações será introduzida, mediante a qual será possível encontrar um sistema de desigualdades que determinam o empacotamento de um número fixo de esferas. Desta forma, resolvemos o problema de empacotamento de esferas através de uma sequência de sistemas de desigualdades. Finalmente, para obter resultados eficientes, minimizaremos a função de sobreposição, usando o método do Lagrangiano Aumentado
Abstract: In this work, we will propose mathematical models for not latticed packing of spheres problems in regions bounded by quadratic in the plane and in the space. A technique to construct representations or parameterizations will be introduced, by which it will be possible to find a system of inequalities which determine the packing of a fixed number of spheres. Thus, we solve the problem of packing spheres through a sequence of systems of inequalities. Finally, to obtain effective results, we will minimize the overlay function using the Augmented Lagrangian Method
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
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Silva, Leandro Tavares da. "Simulação de fluidos via Smoothed Particle Hydrodynamics: formulação variacional, variação de parâmetros e extração de características visuais." Laboratório Nacional de Computação Científica, 2016. https://tede.lncc.br/handle/tede/240.
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The Smoothed Particle Hydrodynamics (SPH) is a Lagrangian and meshless method for discretization of fluid equations. It has been used to fluid simulation in many areas of engineering and applied sciences. This method discretizes the Navier-Stokes equations using a particle system and interpolation theory. In this context, we developed a variational integrator to SPH, using the generalized midpoint rule and fixed point method. Then, we elaborate a implementation of SPH to simulate a quasi-incompressible fluid under influence of disks that rotates with constant angular velocity (N-roll mill setup). The obtained flow patterns are analyzed using Morse and Catastrophe theories. Finally, the two aforementioned works show us the necessity of techniques for comparing fluid simulations. Hence, we developed a framework to generate a visual summary of a computation fluid simulations by adapting techniques of video summary areas. As contribution of this thesis we highlight that the variational integrator has the property of linear momentum conservation being easier to implement than counterpart ones. Also, we emphasize the methodology to analyze the critical points generated by the original implementation of N-roll mill setup using SPH. Besides, the pioneer adaptation of techniques in video summarization, for computation fluid dynamics, allows to capture a detailed picture of important segments of the fluid for both comparison and analysis of the flows.
O método lagrangiano Smoothed Particle Hydrodynamics (SPH) não utiliza malha subjacente para discretização de equações de fluidos e vêm sendo usado para simulações em diversas áreas do conhecimento. Esse método discretiza as equações de Navier-Stokes usando um sistema de partículas e a teoria de interpolação. Neste contexto, desenvolvemos um integrador variacional para o SPH, utilizando a regra do ponto médio generalizada e o método do ponto fixo. Em seguida, elaboramos uma implementação do SPH para simular um fluido quase-incompressível sob a influência de discos que giram com velocidades angulares constantes (\textit{N-roll mill}), denominado nessa tese de problema de N-rolos, e desenvolvemos uma metodologia para analisar os padrões de fluxos gerados. Para esta análise utilizamos a teoria de Morse e a teoria de Catástrofes de René Thom. Finalmente, os dois trabalhos citados nos mostram a necessidade e carência de técnicas para comparação e análise de fluidos. Logo, desenvolvemos um arcabouço para produção de sumários da simulação, adaptando técnicas da área de sumários de vídeo. Como contribuições da tese destacamos que o integrador variacional desenvolvido apresenta facilidade de implementação em relação a esquemas tradicionais e com conservação de momento linear. Destacamos também a metodologia para análise de pontos críticos gerados pela implementação original do problema de N-rolos usando o SPH, bem como a adaptação pioneira de técnicas de sumarização de vídeo para análise de fluidos.
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Penachi, Rian 1989. "Uma introdução à otimização não linear e a solução de problemas simétricos via ALGENCAN." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307618.
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Orientador: Luis Felipe Cesar da Rocha BuenoDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Este trabalho propõe uma abordagem didática acerca de otimização não linear irrestrita e com restrições de igualdade, assim como um guia para o leitor que necessita instalar e utilizar o software ALGENCAN. Prezando por explorar ideias intuitivas do tema, o texto foca em estudar, muitas vezes geometricamente, problemas irrestritos e problemas com restrições de igualdade. Para o caso sem restrições é enfatizada a relação entre métodos de otimização e métodos para zeros de sistemas não lineares, destacando o Método de Newton. Métodos do tipo Lagrangiano Aumentado são o enfoque principal, particularmente em ALGENCAN, que é uma de suas implementações mais bem estabelecidas na literatura. As dificuldades encontradas em métodos computacionais para resolver problemas simétricos de otimização não linear com restrições também são estudadas. São apresentados vários exemplos simples de como a simetria do problema afeta o bom desempenho do método e as alternativas para contornar estes obstáculos. Além do mais, testes mais completos usando a coleção CUTEst comprovam que o algoritmo modificado que introduzimos é, pelo menos, tão competitivo quanto a versão original de ALGENCAN
Abstract: This work proposes a didactic approach concerning nonlinear unconstrained optimization and nonlinear equality constrained optimization, as well as a guide for the readers who need to install and use the ALGENCAN software. Exploring intuitive ideas of the subject, the focus of the text is to study, often in a geometric way, unconstrained problems and problems with equality constraints. For the case of unconstrained problems, it will be emphasized the relationship between optimization methods and methods for nonlinear systems, highlighting the Newton's Method. The main focus will be on the Augmented Lagrangian Method, particularly on ALGENCAN, which is one of the most well-established implementations in the literature. The difficulties found in computational methods to solve symmetric problems of nonlinear constrained optimization will be also studied. It will be shown, through several simple examples, how the symmetry of the problem affects the good performance of the method and the alternatives to overcome these difficulties. Moreover, more complete tests using CUTEst will be done, which will confirm that the modified algorithm introduced by us is, at least, as efficient as the original version of ALGENCAN
Mestrado
Matematica Aplicada e Computacional
Mestre em Matemática Aplicada e Computacional
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Baptista, Edméa Cássia. "Método da função Lagrangiana aumentada-barreira logarítmica para a solução do problema de fluxo de potência ótimo." Universidade de São Paulo, 2001. http://www.teses.usp.br/teses/disponiveis/18/18133/tde-14102015-111239/.
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Neste trabalho propomos uma abordagem para a resolução do problema de fluxo de potência ótimo. Para isso, foram obtidos dados teóricos, a partir de um levantamento bibliográfico, que explicitaram os métodos de penalidade, de barreira, de Newton-Lagrangiano, da função Lagrangiana aumentada e dual-Lagrangiano. Nesta abordagem, as restrições de igualdade são tratadas pelo método de Newton, as restrições canalizadas, de tensão e tap, pelo método da função barreira logarítmica, e as restrições de desigualdade e demais restrições canalizadas, pelo método da função Lagrangiana aumentada. A motivação para este estudo foi a necessidade de manter as variáveis - tensão e tap - dentro de seus limites. Os resultados numéricos apresentados evidenciam o potencial desta metodologia para a resolução de problemas de programação não-linear e, em particular, do problema de fluxo de potência ótimo.A new approach to solving the optimal power flow problem is proposed in this study. The first step in developing this method was to obtain theoretical material from bibliographic survey, which described in detail the penalty method, the barrier method, Newton\'s method, the augmented Lagrangian method end the dual-Lagrangian method. In the new approach, equality constraints are handled by Newton\'s method, the voltage end tap box inequality constraints by the logarithmic barrier method and the inequality constraints and the other box inequality constraints by the augmented Lagrangian method. The motivation for this research was the necessity to keep the voltage and tap variables within their limits. The numerical results demonstrate the potential of this methodology for the solution of nonlinear problems and, in particular, of the optimal power flow problem.
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Hesse, Michel. "Méthode des réseaux de Lagrange en mécanique quantique." Doctoral thesis, Universite Libre de Bruxelles, 2001. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211475.
Full textAbstract:
Les fonctions de Lagrange sont des fonctions indéfiniment dérivables qui s'annulent en tous les points d'un réseau sauf un. Ces fonctions sont utilisées comme fonctions de base d'un calcul variationnel. Les éléments de matrice de ce calcul sont évalués à l'aide de la règle de quadrature de Gauss définie par le réseau de points. Les équations à résoudre prennent ainsi la forme d'équations sur réseau.
La méthode des réseaux de Lagrange allie simplicité et précision. La matrice représentant le potentiel est diagonale et ne dépend que des valeurs prises par le potentiel aux points du réseau. Contrairement à la méthode des différences finies, une expression analytique est obtenue pour la solution. Nous cherchons clans cette thèse à cerner les avantages et inconvénients de la méthode des réseaux de Lagrange, ainsi qu'à étendre son champ d'application en mécanique quantique. Nous montrons notamment que cette méthode peut être reliée à d'autres méthodes sur réseau, telles que les méthodes de la variable discrétisée (DVR) ou du réseau de Fourier, qui sont fort utilisées en physique atomique et moléculaire.
Dans les problèmes à deux corps, nous appliquons la méthode à l'étude des états liés et nous l'étendons au cas des collisions, c'est-à-dire aux états libres. Une nouvelle technique de calcul de la longueur de diffusion et de la portée effective est également considérée. Dans certains cas, la solution exacte du problème à deux corps existe sous forme analytique, ce qui permet une étude de la précision de la méthode en ce qui concerne les valeurs propres et les vecteurs propres de la matrice hamiltonienne. L'extension de la méthode aux problèmes à deux corps régis par une dynamique semi-relativiste est également examinée.
Dans le cas des problèmes à trois corps, nous effectuons une comparaison entre plusieurs systèmes de coordonnées auxquels sont couplés différents réseaux de Lagrange. Les résultats de cette comparaison dépendent de la présence de singularités dans les potentiels, celles-ci pouvant limiter fortement la précision de la méthode.
En physique nucléaire, nous comparons deux approches sur réseaux de Lagrange lors de l'étude de l'état fondamental du noyau 6He. Il s'agit d'un noyau à halo de neutrons, pour lequel il existe une forte probabilité de trouver deux des neutrons loin des autres nucléons. Le noyau 6He peut ainsi être traité comme un système à trois corps, constitué d'une particule alpha et de deux neutrons. Nous étendons également le modèle à trois corps pour ce noyau au cas d'interactions à deux corps plus générales, c'est-à-dire contenant différents opérateurs agissant sur les spins des nucléons.
En physique atomique et moléculaire, où les interactions sont, en première approximation, purement coulombiennes, nous nous sommes intéressé aux états S et P des principaux systèmes à trois corps que sont l'atome d'hélium He, les ions hydrogène H-et positronium Ps-, l'ion moléculaire d'hydrogène HZ et la molécule muonique dt"mu". Les fonctions d'onde approchées obtenues lors de la détermination des états liés sont utilisées pour évaluer des rayons quadratiques moyens et les rayons de masse de ces systèmes.
Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished
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Weerasinghe, Weerasinghe Mudalige Sujith Rohitha. "Application of Lagrangian probability density function approach to turbulent reacting flows." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.392476.
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Madabushi, Ananth R. "Lagrangian Relaxation / Dual Approaches For Solving Large-Scale Linear Programming Problems." Thesis, Virginia Tech, 1997. http://hdl.handle.net/10919/36833.
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This research effort focuses on large-scale linear programming problems that arise in the context of solving various problems such as discrete linear or polynomial, and continuous nonlinear, nonconvex programming problems, using linearization and branch-and-cut algorithms for the discrete case, and using polyhedral outer-approximation methods for the continuous case. These problems arise in various applications in production planning, location-allocation, game theory, economics, and many engineering and systems design problems. During the solution process of discrete or continuous nonconvex problems using polyhedral approaches, one has to contend with repeatedly solving large-scale linear programming(LP) relaxations. Thus, it becomes imperative to employ an efficient method in solving these problems. It has been amply demonstrated that solving LP relaxations using a simplex-based algorithm, or even an interior-point type of procedure, can be inadequately slow ( especially in the presence of complicating constraints, dense coefficient matrices, and ill-conditioning ) in comparison with a Lagrangian Relaxation approach. With this motivation, we present a practical primal-dual subgradient algorithm that incorporates a dual ascent, a primal recovery, and a penalty function approach to recover a near optimal and feasible pair of primal and dual solutions.
The proposed primal-dual approach is comprised of three stages. Stage I deals with solving the Lagrangian dual problem by using various subgradient deflection strategies such as the Modified Gradient Technique (MGT), the Average Direction Strategy (ADS), and a new direction strategy called the Modified Average Direction Strategy (M-ADS). In the latter, the deflection parameter is determined based on the process of projecting the unknown optimal direction onto the space spanned by the current subgradient direction and the previous direction. This projected direction approximates the desired optimal direction as closely as possible using the conjugate subgradient concept. The step-length rules implemented in this regard are the Quadratic Fit Line Search Method and a new line search method called the Directional Derivative Line Search Method in which we start with a prescribed step-length and then ascertain whether to increase or decrease the step-length value based on the right-hand and left-hand derivative information available at each iteration. In the second stage of the algorithm (Stage II), a sequence of updated primal solutions is generated using some convex combinations of the Lagrangian subproblem solutions. Alternatively, a starting primal optimal solution can be obtained using the complementary slackness conditions. Depending on the extent of feasibility and optimality attained, Stage III applies a penalty function method to improve the obtained primal solution toward a near feasible and optimal solution.
We present computational experience using a set of randomly generated, structured, linear programming problems of the type that might typically arise in the context of discrete optimization.Master of Science
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Martinez, Andre Luis Machado. "Metodo lagrangiano aumentado regularizado para problemas com voracidade." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307459.
Full textAbstract:
Orientador: Jose Mario Martinez PerezTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Quando resolvemos problemas de programação não linear por meio de algoritmos que utilizam o Lagrangiano Aumentado, um fenômeno chamado voracidade pode ocorrer. Quando isto ocorre o método busca pontos muito infactíveis com valores de função muito pequenos, em geral, nas primeiras iterações, assim o parâmetro de penalidade cresce excessivamente, de tal forma que prejudica o condicionamento do problema. Neste trabalho 'e sugerida uma abordagem de regularização para superar esta dificuldade. Um método de Lagrangiano Aumentado é definido, com a adição de um termo regularizador que inibe a possibilidade do iterando se afastar demasiadamente do ponto de referência. Provamos convergência e apresentamos exemplos numéricos.
Abstract: When one solves Nonlinear Programming problems by means of algorithms that use merit criteria combining the objective function and penalty feasibility terms, a phenomenon called greediness may occur. Unconstrained minimizers attract the iterates at early stages of the calculations and, so, the penalty parameter needs to grow excessively, in such a way that ill conditioning harms the overall convergence. In this work a regularization approach is suggested to overcome this dificulty. An Augmented Lagrangian method is defined with the addition of a regularization term that inhibits the possibility that the iterates go far from a reference point. Convergence proofs and numerical examples are given.
Doutorado
Doutor em Matemática Aplicada
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Zeferino, Cristiane Lionço. "Estudo do máximo carregamento em sistemas de energia elétrica via método da barreira modificada." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/18/18133/tde-08032007-113530/.
Full textAbstract:
Nesta dissertação é aplicado o método da função Lagrangiana barreira modificada (FLBM), uma variante do método de pontos interiores, para determinação do máximo carregamento em sistemas de energia elétrica. A formulação do problema tem como restrições de igualdade as equações de balanço de potência do sistema, em sua forma parametrizada, e como restrições de desigualdade os limites de tensões nas barras e os limites de geração de potência reativa nas barras com controle de reativo. Os resultados encontrados com a técnica de otimização estática utilizada neste estudo são confrontados com os resultados obtidos com o método primal-dual barreira logarítmica. Para realização dos testes de desempenho da metodologia proposta, utilizou-se como padrão os sistemas do IEEE de 14, 57 e 118 barras. Os testes demonstraram a robustez e a eficiência do algoritmo proposto.In this work the modified barrier Lagrangian function (MBLF) method, a variant of the interior point method. The formulation of the problem will have as constraints of equality the power system swinging equations, in a parametrized form, and as inequality constraints the voltage limits in the buses and the reactive generation limits in the buses with reactive control. The results found with the static optimization technique used in this study are confronted with the results obtained with the primal-dual barrier logarithmic method. The performance of the method is illustrated using as pattern the systems IEEE 14, 57 and 118 bars. The tests demonstrated the robustness and the efficiency of the proposed algorithm.
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Sadjadi, Seyed Jafar. "Nonlinear programming using an expanded Lagrangian function, a water resources management case study." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0014/NQ30640.pdf.
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Nascimento, Clebea Araújo. "Abordagem do problema de fluxo de potência ótimo por métodos de programação não-linear via penalidade quadrática e Função Lagrangeana Aumentada." Universidade de São Paulo, 1997. http://www.teses.usp.br/teses/disponiveis/18/18133/tde-22012018-113127/.
Full textAbstract:
Neste trabalho são estudadas três metodologias de otimização não-linear: o Método da Função Lagrangeana, o Método da Função Penalidade e o Método da Função Lagrangeana Aumentada. Com o estudo da Função Lagrangeana e do Método da Função Penalidade, foi possível alcançar a formulação da Função Lagrangeana Aumentada com o objetivo de resolver problemas de programação não-linear não-convexos. Testes numéricos são apresentados para o problema não-convexo de programação não-linear conhecido como Fluxo de Potência Ótimo.In this dissertation, three nonlinear optimization methodologies are studied: the Lagrangian Function Method, the Penalty Function Method and Augmented Lagrangian Function Method. Through the studies ofthe Lagrangian Function and the Penalty function Method, it was possible to reach the formulation of the Augmented Lagrangian Function aiming to solve nonlinear nonconvex programming problems. Numerical tests are presented for the nonconvex nonlinear programming problem known as optimal power flow.
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Poletto, Vinicius Gustavo. "Modelagem e simulação numérica da deposição de partículas em meio poroso: um estudo da formação de reboco durante a perfuração de poços de petróleo." Universidade Tecnológica Federal do Paraná, 2017. http://repositorio.utfpr.edu.br/jspui/handle/1/2989.
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O fenômeno de perda de circulação é consequência da perfuração de poços de petróleo e gás em substratos permeáveis e é caracterizado pelo influxo de fluido de perfuração da região anular para a formação. Além dos custos adicionais relacionados com a necessidade constante de reposição do fluido perdido, danos à formação nas adjacências do poço são de ocorrência comum. Uma potencial solução é a adição de materiais de perda de circulação (LCM’s) ao fluido de perfuração para que uma camada de reboco se forme na parede do poço em filtração dinâmica. Neste trabalho, o escoamento bifásico líquido-sólido é simulado numericamente através de uma abordagem de Euler-Lagrange para representar o crescimento do reboco na interface poço-formação. A região anular do poço é idealizada como um canal vertical de seção transversal retangular em contato com um meio poroso anisotrópico, o qual é concebido na escala do poro (heterogêneo) como um arranjo de cilindros alternados. O escoamento particulado é ascendente e eventualmente as partículas, as quais representam o LCM, abandonam o canal adentrando o meio poroso onde pode ocorrer a geração do reboco. A simulação é realizada através do Método de Fase Discreta Densa (DDPM) no qual as equações da fase sólida e fluida são solucionadas separadamente. O Método dos Elementos Discretos (DEM) é empregado para calcular as interações de contato (colisão e atrito). A caracterização do combate à perda de circulação é realizada através da redução da vazão de fuga ao longo do tempo. Resultados mostram o efeito da variação do número de Reynolds no canal (125, 250, 500), da vazão inicial de fuga (5, 10, 20%), do diâmetro das partículas (0,50; 0,75; 1,00 mm), da razão de massa específica partícula-fluido (1,5; 2,5) e da configuração do meio poroso (porosidade, número de cilindros e garganta de poro). A eficiência do reboco na redução da vazão de fuga recai na formação de um plugue de partículas que seja capaz de obturar toda a altura do meio poroso, não permitindo que haja gargantas de poros desobstruídas. Tal aspecto é favorecido pela redução do diâmetro e da razão de massa específica, bem como pelo aumento do Reynolds e da vazão inicial de fuga.The lost circulation is a consequence of the well drilling in a permeable substrate, being characterized by the drilling fluid influx to the porous formation. Despite the additional costs associated with the need of continuous fluid replacement, another misfortune is the irreversible formation damage due to the fluid invasion, which may reflect negatively throughout the productive life of the well. Therefore, it is of utter importance to make use of preventive and corrective techniques, like the addition of lost circulation materials (LCM) to the drilling fluid. The LCM particles deposit over the porous formation under dynamic filtration and create a mud cake (filter cake) that helps diminishing the fluid invasion flow rate. In this work, the liquid-solid two-phase flow is numerically simulated via an Euler-Lagrange approach to represent the mud cake growth. The well annular region is considered as a vertical channel bounded by an anisotropic porous formation. The porous medium is conceived in the pore-scale as a periodic array of staggered cylinders. The fluid flows upward through the channel carrying the solid particles that mimic the LCM’s. The particles might eventually get into the porous formation and deposit, creating the mud cake. The equations for the fluid flow and for the particles movement are solved separately via the Dense Discrete Phase Model (DDPM). The particle-particle and particle-wall interactions like collision and friction are calculated via the Discrete Element Methods that is coupled to the DDPM. The effectiveness of the lost circulation mitigation is evaluated mainly by the decrease in the fluid invasion flow rate over time. The results demonstrate the influence of the variation of the Reynolds number on the channel (125, 250, 500), the initial fluid invasion flow rate (5, 10, 20%), the particles diameter (0.50, 0.75, 1.00 mm), the particle-fluid specific mass ratio (1.5, 2.5) and the configuration of the porous medium (porosity, number of cylinders and pore throat).
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Masiero, Maria Cláudia Sávio. "O método da função lagrangiana aumentada barreira modificada para a resolução do fluxo de potência ótimo /." Bauru : [s.n.], 2011. http://hdl.handle.net/11449/87202.
Full textAbstract:
Orientador: Edméa Cássia BaptistaBanca: Vanusa Alves de Sousa
Banca: Leonardo Nepomuceno
Resumo: Este trabalho propõe uma abordagem que utiliza uma associação dos métodos de barreira modificada e da Lagrangiana aumentada para a resolução do problema de fluxo de potência ótimo. Para isso, foi realizado um levantamento bibliográfico que explicitou os métodos de Newton-Lagrangiano, de barreira modificada e da função lagrangiada aumentada. Na abordagem proposta, as restrições canalizadas são desmembradas em duas desigualdades. Estas são transformadas em igualdades a partir do acréscimo de variáveis de folga ou de excesso positivas, as quais são tratadas pela função barreira modificada. As restrições de igualdade originais do problema são tratadas pelo método da função Lagrangiana aumentada e as igualdades restantes através da função Lagrangiana. As condições necessárias de primeira ordem são aplicadas resultando num sistema não linear o qual é resolvido pelo método de Newton. A eficiência do método foi verificada utilizando um exemplo matemático e em problemas de fluxo de potência ótimo
Abstract: This work proposes an approach that uses an association of the modified barrier method and augmented Lagrangian method for the solution of the optimal power flow problem. On this purpose, a bibliographical review was accomplished the methods Newton-Lagrangian, modified barrier and augmented Lagrangian function. In this approach, the bounded constraints are transformed in equalities by additing the non-negative slack variables. Those slack variables are handled by the modified barrier function. The original equality constrains of the problem are handled by the method of augmented Lagrangian function and the remaining equalities are handled by the Lagrangian function. The first order necessary conditions are applied resulting a nonlinear system which is solved by Newton's method. The effectiveness of the proposed approach has been examined by solving a mathematical example and optimal power flow problems
Mestre
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Castelani, Emerson Vitor. "Um metodo do tipo lagrangiano aumentado com região de confiança." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307457.
Full textAbstract:
Orientador: Jose Mario Martinez PerezTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Ao resolver problemas de programação não linear usando métodos do tipo Lagrangiano Aumentado, um fenômeno chamado voracidade pode ocorrer. Quando este fenômeno ocorre, o método busca pontos muito infactíveis com valor de função objetivo muito pequeno. Tais fatos ocorrem, em geral, na primeiras iterações e então, o parâmetro de penalidade precisa crescer excessivamente, tornado os subproblemas mal condicionados, prejudicando assim a convergência. Desta forma, o propósito deste trabalho é adicionar restrições de caixas adaptativas (região de confiança) a cada subproblema em cada iteração externa, de modo que, a distância entre dois iterando consecutivos das iterações externas é controlada. O novo método inibe a possibilidade do fenômeno de voracidade. Resultados de convergência, limitação de parâmetro de penalidade e exemplos numéricos são apresentados
Abstract: When we solve nonlinear programming problems by means of algorithms of kind of Augmented Lagrangian, a phenomenon called greediness may occur. Unconstrained minimizers attract the iterates at early stages of the calculations and, so, the penalty parameter needs to grow excessively, in such a way that ill-conditioning harms the overall convergence. In this sense, the proposal of this work is to add an adaptive artificial box constraint (trust-region) to the subproblem at every outer iteration, in such a way that the distance between consecutive outer iterates is controlled. The new method inhibits the possibility of greediness phenomenon. Convergence proofs and numerical examples are given
Doutorado
Otimização
Doutor em Matemática Aplicada
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Manomaiphiboon, Kasemsan. "Estimation of Emission Strength and Air Pollutant Concentrations by Lagrangian Particle Modeling." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5141.
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A Lagrangian particle model was applied to estimating emission strength and air pollutant concentrations specifically for the short-range dispersion of an air pollutant in the atmospheric boundary layer. The model performance was evaluated with experimental data. The model was then used as the platform of parametric uncertainty analysis, in which effects of uncertainties in five parameters (Monin-Obukhov length, friction velocity, roughness height, mixing height, and the universal constant of the random component) of the model on mean ground-level concentrations were examined under slightly and moderately stable conditions. The analysis was performed under a probabilistic framework using Monte Carlo simulations with Latin hypercube sampling and linear regression modeling. In addition, four studies related to the Lagrangian particle modeling was included. They are an alternative technique of formulating joint probability density functions of velocity for atmospheric turbulence based on the Koehler-Symanowski technique, analysis of local increments in a multidimensional single-particle Lagrangian particle model using the algebra of Ito integrals and the Wagner-Platen formula, analogy between the diffusion limit of Lagrangian particle models and the classical theory of turbulent diffusion, and evaluation of some proposed forms of the Lagrangian velocity autocorrelation of turbulence.
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Mahdavi, Mostafa. "Study of flow and heat transfer features of nanofluids using multiphase models : eulerian multiphase and discrete Lagrangian approaches." Thesis, University of Pretoria, 2016. http://hdl.handle.net/2263/61309.
Full textAbstract:
Choosing correct boundary conditions, flow field characteristics and employing right
thermal fluid properties can affect the simulation of convection heat transfer using
nanofluids. Nanofluids have shown higher heat transfer performance in comparison with
conventional heat transfer fluids. The suspension of the nanoparticles in nanofluids
creates a larger interaction surface to the volume ratio. Therefore, they can be
distributed uniformly to bring about the most effective enhancement of heat transfer
without causing a considerable pressure drop. These advantages introduce nanofluids as
a desirable heat transfer fluid in the cooling and heating industries. The thermal effects of
nanofluids in both forced and free convection flows have interested researchers to a great
extent in the last decade.
Investigating the interaction mechanisms happening between nanoparticles and base
fluid is the main goal of the study. These mechanisms can be explained via different
approaches through some theoretical and numerical methods. Two common approaches
regarding particle-fluid interactions are Eulerian-Eulerian and Eulerian-Lagrangian.
The dominant conceptions in each of them are slip velocity and interaction forces
respectively. The mixture multiphase model as part of the Eulerian-Eulerian approach
deals with slip mechanisms and somehow mass diffusion from the nanoparticle phase to
the fluid phase. The slip velocity can be induced by a pressure gradient, buoyancy, virtual
mass, attraction and repulsion between particles. Some of the diffusion processes can be
caused by the gradient of temperature and concentration. The discrete phase model (DPM) is a part of the Eulerian-Lagrangian approach. The
interactions between solid and liquid phase were presented as forces such as drag,
pressure gradient force, virtual mass force, gravity, electrostatic forces, thermophoretic
and Brownian forces. The energy transfer from particle to continuous phase can be
introduced through both convective and conduction terms on the surface of the particles.
A study of both approaches was conducted in the case of laminar and turbulent forced
convections as well as cavity flow natural convection. The cases included horizontal and
vertical pipes and a rectangular cavity. An experimental study was conducted for cavity
flow to be compared with the simulation results. The results of the forced convections
were evaluated with data from literature. Alumina and zinc oxide nanoparticles with
different sizes were used in cavity experiments and the same for simulations. All the
equations, slip mechanisms and forces were implemented in ANSYS-Fluent through some
user-defined functions.
The comparison showed good agreement between experiments and numerical results.
Nusselt number and pressure drops were the heat transfer and flow features of nanofluid
and were found in the ranges of the accuracy of experimental measurements. The findings
of the two approaches were somehow different, especially regarding the concentration
distribution. The mixture model provided more uniform distribution in the domain than
the DPM. Due to the Lagrangian frame of the DPM, the simulation time of this model
was much longer. The method proposed in this research could also be a useful tool for
other areas of particulate systems.Thesis (PhD)--University of Pretoria, 2016.
Mechanical and Aeronautical Engineering
PhD
Unrestricted
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Modena, Stefano. "Interaction functionals, Glimm approximations and Lagrangian structure of BV solutions for Hyperbolic Systems of Conservation Laws." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4873.
Full textAbstract:
This thesis is a contribution to the mathematical theory of Hyperbolic Conservation Laws. Three are the main results which we collect in this work. The first and the second result (denoted in the thesis by Theorem A and Theorem B respectively) deal with the following problem. The most comprehensive result about existence, uniqueness and stability of the solution to the Cauchy problem \begin{equation}\tag{$\mathcal C$}
\label{E:abstract} \begin{cases} u_t + F(u)_x = 0, \\u(0, x) = \bar u(x), \end{cases}
\end{equation} where $F: \R^N \to \R^N$ is strictly hyperbolic, $u = u(t,x) \in \R^N$, $t \geq 0$, $x \in \R$, $\TV(\bar u) \ll 1$, can be found in [Bianchini, Bressan 2005], where the well-posedness of \eqref{E:abstract} is proved by means of vanishing viscosity approximations. After the paper [Bianchini, Bressan 2005], however, it seemed worthwhile to develop a \emph{purely hyperbolic} theory (based, as in the genuinely nonlinear case, on Glimm or wavefront tracking approximations, and not on vanishing viscosity parabolic approximations) to prove existence, uniqueness and stability results. The reason of this interest can be mainly found in the fact that hyperbolic approximate solutions are much easier to study and to visualize than parabolic ones. Theorems A and B in this thesis are a contribution to this line of research. In particular, Theorem A proves an estimate on the change of the speed of the wavefronts present in a Glimm approximate solution when two of them interact; Theorem B proves the convergence of the Glimm approximate solutions to the weak admissible solution of \eqref{E:abstract} and provides also an estimate on the rate of convergence. Both theorems are proved in the most general setting when no assumption on $F$ is made except the strict hyperbolicity. The third result of the thesis, denoted by Theorem C, deals with the Lagrangian structure of the solution to \eqref{E:abstract}. The notion of Lagrangian flow is a well-established concept in the theory of the transport equation and in the study of some particular system of conservation laws, like the Euler equation. However, as far as we know, the general system of conservations laws \eqref{E:abstract} has never been studied from a Lagrangian point of view. This is exactly the subject of Theorem C, where a Lagrangian representation for the solution to the system \eqref{E:abstract} is explicitly constructed. The main reasons which led us to look for a Lagrangian representation of the solution of \eqref{E:abstract} are two: on one side, this Lagrangian representation provides the continuous counterpart in the exact solution of \eqref{E:abstract} to the well established theory of wavefront approximations; on the other side, it can lead to a deeper understanding of the behavior of the solutions in the general setting, when the characteristic field are not genuinely nonlinear or linearly degenerate.
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Floratos, Ioannis. "Multi-Skyrmion solutions of a sixth order Skyrme model." Thesis, Durham University, 2001. http://etheses.dur.ac.uk/3988/.
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In this Thesis, we study some of the classical properties of an extension of the Skyrme model defined by adding a sixth order derivative term to the Lagrangian. In chapter 1, we review the physical as well as the mathematical motivation behind the study of the Skyrme model and in chapter 2, we give a brief summary of various extended Skyrme models that have been proposed over the last few years. We then define a new sixth order Skyrme model by introducing a dimensionless parameter λ that denotes the mixing between the two higher order terms, the Skyrme term and the sixth order term. In chapter 3 we compute numerically the multi-skyrmion solutions of this extended model and show that they have the same symmetries with the usual skyrmion solutions. In addition, we analyse the dependence of the energy and radius of these classical solutions with respect to the coupling constant λ. We compare our results with experimental data and determine whether this modified model can provide us with better theoretical predictions than the original one. In chapter 4, we use the rational map ansatz, introduced by Houghton, Manton and Sutcliffe, to approximate minimum energy multi-skyrmion solutions with B ≤ 9 of the SU(2) model and with B ≤ 6 of the SU(3) model. We compare our results with the ones obtained numerically and show that the rational map ansatz works just as well for the generalised model as for the pure Skyrme model, at least for B ≤ 5. In chapter 5, we use a generalisation of the rational map ansatz, introduced by loannidou, Piette and Zakrzewski, to construct analytically some topologically non-trivial solutions of the extended model in SU(3). These solutions are spherically symmetric and some of them can be interpreted as bound states of skyrmions. Finally, we use the same ansatz to construct low energy configurations of the SU(N) sixth order Skyrme model.
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Masiero, Maria Cláudia Sávio [UNESP]. "O método da função lagrangiana aumentada barreira modificada para a resolução do fluxo de potência ótimo." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/87202.
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Universidade Estadual Paulista (UNESP)
Este trabalho propõe uma abordagem que utiliza uma associação dos métodos de barreira modificada e da Lagrangiana aumentada para a resolução do problema de fluxo de potência ótimo. Para isso, foi realizado um levantamento bibliográfico que explicitou os métodos de Newton-Lagrangiano, de barreira modificada e da função lagrangiada aumentada. Na abordagem proposta, as restrições canalizadas são desmembradas em duas desigualdades. Estas são transformadas em igualdades a partir do acréscimo de variáveis de folga ou de excesso positivas, as quais são tratadas pela função barreira modificada. As restrições de igualdade originais do problema são tratadas pelo método da função Lagrangiana aumentada e as igualdades restantes através da função Lagrangiana. As condições necessárias de primeira ordem são aplicadas resultando num sistema não linear o qual é resolvido pelo método de Newton. A eficiência do método foi verificada utilizando um exemplo matemático e em problemas de fluxo de potência ótimo
This work proposes an approach that uses an association of the modified barrier method and augmented Lagrangian method for the solution of the optimal power flow problem. On this purpose, a bibliographical review was accomplished the methods Newton-Lagrangian, modified barrier and augmented Lagrangian function. In this approach, the bounded constraints are transformed in equalities by additing the non-negative slack variables. Those slack variables are handled by the modified barrier function. The original equality constrains of the problem are handled by the method of augmented Lagrangian function and the remaining equalities are handled by the Lagrangian function. The first order necessary conditions are applied resulting a nonlinear system which is solved by Newton's method. The effectiveness of the proposed approach has been examined by solving a mathematical example and optimal power flow problems
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Ferreira, Vitor Maciel Vilela. "A hybrid les / lagrangian fdf method on adaptive, block-structured mesh." Universidade Federal de Uberlândia, 2015. https://repositorio.ufu.br/handle/123456789/14982.
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Fundação de Amparo a Pesquisa do Estado de Minas GeraisEsta dissertação é parte de um amplo projeto de pesquisa, que visa ao desenvolvimento de uma plataforma computacional de dinâmica dos fluidos (CFD) capaz de simular a física de escoamentos que envolvem mistura de várias espécies químicas, com reação e combustão, utilizando um método hibrido Simulação de Grandes Escalas (LES) / Função Densidade Filtrada (FDF) Lagrangiana em malha adaptativa, bloco-estruturada. Uma vez que escoamentos com mistura proporcionam fenômenos que podem ser correlacionados com a combustão em escoamentos turbulentos, uma visão global da fenomenologia de mistura foi apresentada e escoamentos fechados, laminar e turbulento, que envolvem mistura de duas espécies químicas inicialmente segregadas foram simulados utilizando o código de desenvolvimento interno AMR3D e o código recentemente desenvolvido FDF Lagrangiana de composição. A primeira etapa deste trabalho consistiu na criação de um modelo computacional de partículas estocásticas em ambiente de processamento distribuído. Isto foi alcançado com a construção de um mapa Lagrangiano paralelo, que pode gerenciar diferentes tipos de elementos lagrangianos, incluindo partículas estocásticas, particulados, sensores e nós computacionais intrínsecos dos métodos Fronteira Imersa e Acompanhamento de Interface. O mapa conecta informações Lagrangianas com a plataforma Euleriana do código AMR3D, no qual equações de trans- porte são resolvidas. O método FDF Lagrangiana de composição realiza cálculos algébricos sobre partículas estocásticas e provê campos de composição estatisticamente equivalentes aos obtidos quando se utiliza o método de Diferenças Finitas para solução de equações diferenciais parciais; a técnica de Monte Carlo foi utilizada para resolver um sistema derivado de equações diferenciais estocásticas (SDE). Os resultados concordaram com os benchmarks, que são simulações baseadas em plataforma de Diferenças Finitas para solução de uma equação de transporte de composição filtrada.
This master thesis is part of a wide research project, which aims at developing a com- putational fluid dynamics (CFD) framework able to simulate the physics of multiple-species mixing flows, with chemical reaction and combustion, using a hybrid Large Eddy Simulation (LES) / Lagrangian Filtered Density Function (FDF) method on adaptive, block-structured mesh. Since mixing flows provide phenomena that may be correlated with combustion in turbulent flows, we expose an overview of mixing phenomenology and simulated enclosed, ini- tially segregated two-species mixing flows, at laminar and turbulent states, using the in-house built AMR3D and the developed Lagrangian composition FDF codes. The first step towards this objective consisted of building a computational model of notional particles transport on distributed processing environment. We achieved it constructing a parallel Lagrangian map, which can hold different types of Lagrangian elements, including notional particles, particu- lates, sensors and computational nodes intrinsic to Immersed Boundary and Front Tracking methods. The map connects Lagrangian information with the Eulerian framework of the AMR3D code, in which transport equations are solved. The Lagrangian composition FDF method performs algebraic calculations over an ensemble of notional particles and provides composition fields statistically equivalent to those obtained by Finite Differences numerical solution of partially differential equations (PDE); we applied the Monte Carlo technique to solve a derived system of stochastic differential equations (SDE). The results agreed with the benchmarks, which are simulations based on Finite Differences framework to solve a filtered composition transport equation.
Mestre em Engenharia Mecânica
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Zeferino, Cristiane Lionço. "Avaliação e controle de margem de carregamento em sistemas elétricos de potência." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/18/18154/tde-05052011-091651/.
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Neste trabalho é proposta a determinação do ponto de Máximo Carregamento (PMC) em sistemas elétricos de potência por meio do método da Função Lagrangiana Barreira Modificada (FLBM), uma variante do método de Pontos Interiores (PI). Também por meio do método da FLBM, busca-se determinar qual é a barra, para cada sistema, que apresenta a maior sensibilidade em relação ao fator de carregamento, ou seja, qual seria a primeira barra que deveria sofrer corte de carga a fim de aumentar a margem de carregamento do sistema e, assim, evitar o colapso de tensão. Para comprovação dos resultados obtidos por meio do método da FLBM utiliza-se a técnica de Análise de Sensibilidade (AS). A formulação do problema tem como restrições de igualdade as equações de balanço de potência do sistema elétrico e como restrições de desigualdade os limites de tensões nas barras, assim como os limites de geração de potência reativa nas barras com controle da referida potência. Estudos de casos foram realizados em um sistema de 3 barras e nos sistemas IEEE 14, 57, 118 e 300 barras; tais estudos demonstraram a robustez e a eficiência dos algoritmos propostos.This work proposes the determination of the Maximum Loading Point (MLP) in electric power system via Lagrangian Modified Barrier Function (LMBF) method, a variant of Interior Point (IP). The LMBF method is also used to determine which bus, for each system, has the highest sensitivity of load factor, i.e., which bus would be the first to have load shedding in order to increase the loading margin system and thus prevent voltage collapse. To validate this approach, the Sensitivity Analysis (SA) technique was used for the confirmation of the results obtained by the LMBF method. The formulation of the problem considered the equations of power balance of the electrical system equality constraints, and the buses voltage magnitude limits, as well as the limits of reactive power control at the buses of that power inequality constraints. Case studies were conducted in a system of 3 buses and IEEE systems 14, 57, 118 and 300 buses, demonstrating the robustness and efficiency of the proposed algorithms.
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Ozdaryal, Burak. "Exterior Penalty Approaches for Solving Linear Programming Problems." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/33862.
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In this research effort, we study three exterior penalty function approaches for solving linear programming problems. These methods are an active set l2 penalty approach (ASL2), an inequality-equality based l2 penalty approach (IEL2), and an augmented Lagrangian approach (ALAG). Particular effective variants are presented for each method, along with comments and experience on alternative algorithmic strategies that were empirically investigated. Our motivation is to examine the relative performance of these different approaches based on the basic l2 penalty function in order to provide insights into the viability of these methods for solving linear programs. To test the performance of these algorithms, a set of randomly generated problems as well as a set of NETLIB test problems from the public domain are used. By way of providing a benchmark for comparisons, we also solve the test problems using CPLEX 6.0, an advanced simplex implementation. While a particular variant (ALAG2) of ALAG performed the best for randomly generated test problems, ASL2 performed the best for the NETLIB test problems. Moreover, for test problems having only equality constraints, IEL2, and ASL2 (which is a finer-tuned version of IEL2 in this case) were comparable and yielded a second-best performance in comparison with ALAG2. Furthermore, a set of problems with relatively higher density parameter values, as well as a set of low-density problems were used to determine the effect of density on the relative performances of these methods. This experiment revealed that for linear programs with a high density parameter, ASL2 is the best alternative among the tested algorithms; whereas, for low-density problems ALAG2 is the fastest method. Moreover, although our implementation was rudimentary in comparison with CPLEX, all of the tested methods attained a final solution faster than CPLEX for the set of large-scale low-density problems, sometimes as fast as requiring only 16-23% of the effort consumed by CPLEX. Average rank tests based on the computational results obtained are performed using two different statistics, that assess the speed of convergence and the quality or accuracy of the solution, in order to determine the relative effectiveness of the algorithms and to validate our conclusions. Overall, the results provide insights into selecting algorithmic strategies based on problem structure and indicate that while this class of methods is viable for computing near optimal solutions, more research is needed to design robust and competitive exterior point methods for solving linear programming problems. However, the use of the proposed variant of the augmented Lagrangian method to solve large-scale low-density linear programs is promising and should be explored more extensively.Master of Science
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Vasconcelos, Fillipe Matos de. "Uma abordagem Lagrangiana na otimização Volt/VAr em redes de distribuição." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/18/18154/tde-06062017-072758/.
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Este projeto de pesquisa propõe desenvolver um novo modelo e uma nova abordagem para a resolução do problema da otimização Volt/VAr em redes de distribuição de energia elétrica. A otimização Volt/VAr consiste em, basicamente, determinar os ajustes das variáveis de controle tais como bancos de capacitores chaveados, transformadores com comutação de tap sob carga e reguladores de tensão, de modo a satisfazer, simultaneamente, as restrições de carga e de operação para um dado objetivo operacional. Esse problema, matematicamente, foi formulado como um problema de programação não linear, multiperíodo, e com variáveis contínuas e discretas. Algoritmos de programação não linear foram utilizados com o intuito de aproveitar as vantagens das matrizes altamente esparsas montadas ao longo do método de solução. Para utilizar tais algoritmos, as variáveis discretas são tratadas como contínuas por meio da utilização de funções senoidais que penalizam a função objetivo do problema original enquanto estas não convergirem para algum dos pontos pré-definidos no seu domínio. O caráter multiperíodo do problema, contudo, refere-se à consideração de uma restrição que relaciona os ajustes das variáveis de controle para sucessivos intervalos de tempo na medida em que limita o número de operações de chaveamento desses dispositivos para um período de 24-horas. O estudo fundamenta-se, metodologicamente, em métodos do tipo Primal-Dual Barreira-Logarítmica. Para demonstrar a eficiência do modelo proposto e a robustez dessa abordagem, a partir de dados teóricos obtidos de levantamentos bibliográficos, testes foram realizados em sistemas-teste de 10, 69 e 135 barras, e em um sistema de 442 barras do noroeste do Reino Unido. As implementações computacionais foram feitas nos softwares MATLAB, AIMMS e GAMS, utilizando o solver IPOPT como método de solução. Os resultados mostram que a abordagem proposta para a resolução do problema de programação não linear é eficaz para tratar adequadamente todas as variáveis presentes em problemas de otimização Volt/VAr.This work proposes a new model and a new approach for solving the Volt / VAr optimization problem in distribution systems. The Volt/VAr optimization consists, basically, to determine the settings of the control variables of switched capacitor banks, on-load tap changer transformers and voltage regulators, in order to satisfy both the load and operational constraints, to a given operational objective. The problem is formulated as a nonlinear programming problem, multiperiod, and with continuous and discrete variables. Nonlinear programming algorithms were used in order to take advantage of the highly sparse matrices built along the solution method. The discrete variables are treated as continuous along the solution method by means of the use of sinusoidal functions that penalize the original objective function while the control variables do not converge to any of the predefined discrete points in its domain. The multiperiod, or dynamic, characteristic of the problem, however, refers to the use of a constraint that relates the settings of the control variables for successive time intervals that limits the control devices switching operations number for a period of 24-hours. The study is based, methodologically, on Primal-Dual Logarithmic Barrier method. To demonstrate the effectiveness of the proposed model and the robustness of this approach, the data were obtained from theoretical literature surveys, and tests were performed on test-systems of 10, 69 and 135 buses, and in a 442 buses located in the Northwest of the United Kingdom. The computational implementation was accomplished in the softwares MATLAB, AIMMS and GAMS, using the IPOPT solver as solution method. The results have shown the approach for solving nonlinear programming problems is effective to appropriate cope with all the variables presented in Volt/VAr optimization problems.