Orientadores: Aurelio Ribeiro Leite de Oliveira, Carla Taviane Lucke da Silva Ghidini / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T05:01:05Z (GMT). No. of bitstreams: 1 Berti_LilianFerreira_M.pdf: 11222489 bytes, checksum: 8a581cf3762be9e96b4f77b7206e3112 (MD5) Previous issue date: 2012 / Resumo: Os métodos de pontos interiores têm sido amplamente utilizados para determinar a solução de problemas de programação linear de grande porte. O método preditor corretor, dentre todas as variações de métodos de pontos interiores, é um dos que mais se destaca, devido à sua eficiência e convergência rápida. Este método, em cada iteração, necessita resolver dois sistemas lineares para determinar a direção preditora corretora. Resolver estes sistemas lineares corresponde ao passo que requer mais tempo de processamento, devendo assim ser realizada de forma eficiente. Para resolver estes sistemas lineares a abordagem mais utilizada é a fatoração de Cholesky. No entanto, realizar a fatoração de Cholesky em cada iteração tem um alto custo computacional. Dessa forma, na busca de redução de esforços, precisamente, na redução do número de iterações foi desenvolvida a iteração continuada. Iteração continuada é uma iteração subsequente, realizada após o cálculo da direção preditora corretora, onde é determinada uma nova direção sem que seja necessário realizar uma nova fatoração de Cholesky. Os resultados computacionais dos testes realizados, principalmente em problemas de médio e grande porte mostraram que esta abordagem obtém bom desempenho em comparação com o método preditor corretor / Abstract: Interior point methods have been widely used in the solution of large linear programming problems. The predictor corrector method, among ali interior point variants, is one of mostly used due to its efficiency and convergence properties. This method needs the solution of two linear systems to determine the predictor corrector direction, in each iteration. Solving such systems corresponds to the step which requires more processing time. Therefore, it should be done efficiently. The most common approach to solve the linear systems is the Cholesky factorization, demanding in each iteration a high computacional effort. Thus, in search of effort reduction, in particular, to reduce the iterations number continued iteration was developed. The continued iteration is a subsequent iteration performed after the predictor corrector direction is computed, where a new direction is calculated without need to of Cholesky refactorization. The numerical tests show that the continued iteration performs better in comparison with the preditor corretor method / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

Orientadores: Aurélio Ribeiro Leite de Oliveira, Marta Ines Velazco Fontova / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T12:49:39Z (GMT). No. of bitstreams: 1 Coelho_AlessandroFonsecaEsteves_M.pdf: 2659631 bytes, checksum: fc1bec925179612ee07a4aaef7092d8a (MD5) Previous issue date: 2011 / Resumo: Um método frequentemente utilizado para a solução de problemas de programação linear é o método de pontos interiores. Nestes métodos precisamos resolver sistemas lineares para calcular a direção de Newton a cada iteração. A solução desses sistemas consiste no passo de maior esforço computacional nos métodos de pontos interiores. A fatoração de Cholesky é a opção mais utilizada para resolver estes sistemas. Contudo, quando trabalhamos com problemas de grande porte, esta fatoração pode ser densa e torna-se inviável trabalhar com esses métodos. Nestes casos, uma boa opção consiste no uso de métodos iterativos precondicionados. Estudos anteriores utilizam o método dos gradientes conjugados precondicionado para obter uma solução destes sistemas. Particularmente, os sistemas originados dos métodos de pontos interiores, são, naturalmente, sistemas de equações normais. Porém, a versão padrão do método dos gradientes conjugados, não considera a estrutura de equações normais do sistema. Neste trabalho propomos a utilização de duas versões do método de gradientes conjugados precondicionado que consideram a estrutura de equações normais destes sistemas. Estas versões serão comparadas com a versão de gradientes conjugados precondicionada que não considera a estrutura de equações normais do sistema. Resultados numéricos com problemas de grande porte mostram que uma dessas versões é competitiva em relação à versão padrão / Abstract: An often used method for solving linear programming problems is the interior point method. In these methods we need to solve linear systems to compute the Newton search direction at each iteration. The solution of these systems is the procedure of most computational effort in interior point methods. The Cholesky factorization is the most often used method to solve these systems. However, when dealing with large scale problems, this factorization can be dense and it become impossible to apply such methods. In such cases, a good option is the use of preconditioned iterative methods. Previous studies have used the preconditioned conjugate gradient method to find the solution of these systems. Particularly, the systems arising from interior point methods are, naturally, systems of normal equations type. Nevertheless, the standard version of the conjugate gradient method, does not take into account the normal equations system structure. This study proposes the use of two versions of preconditioned conjugate gradient method considering the normal equations structure of these systems. These versions are compared with the preconditioned conjugate gradient version that does not consider that structure. Numerical results with large scale problems show that one of these versions is competitive with the standard one / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

In this work, it is presented the multiple objective networkflow problems. This kind of problem is converted into singleo bjective problem and solved by using the primal dual interior point method. The linear system associated to the interior point method is solved by using the Cholesky decomposition, implemented in MATLAB code. Networks of different dimensions are constructed and the computational results show the efficiency of the mentioned interior point method for solving multiple objective network flow problems.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-07-11T12:50:27Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) DissertaçãoRodrigoNunesdeMelo.pdf: 5589879 bytes, checksum: e851e203ef8b11b9711c04c1c34a7ede (MD5) / Made available in DSpace on 2017-07-11T12:50:27Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) DissertaçãoRodrigoNunesdeMelo.pdf: 5589879 bytes, checksum: e851e203ef8b11b9711c04c1c34a7ede (MD5) Previous issue date: 2016-06-17 / FACEPE / O planejamento da operação de um sistema elétrico de potência está diretamente relacionado com o despacho de usinas hidrelétricas e termelétricas. As características geográficas do Brasil contribuem para que o parque gerador seja predominantemente hidráulico. Devido à grande dimensão dos sistemas elétricos, a otimização do problema de despacho hidrotérmico é uma tarefa extremamente complexa que pode ser realizada de modo eficiente, buscando otimizar a operação dos reservatório das usinas hidráulicas, onde o objetivo é a redução do custo na geração térmica necessária para atendimento à carga e eventuais déficits de energia, além de maior nível de segurança. O presente trabalho aborda o desenvolvimento e a implementação de um software para resolução do problema do despacho hidrotérmico em três patamares de carga a ser atendido. Neste trabalho o problema de despacho foi formulado como um problema de programação linear, que por sua vez foi solucionado pelos métodos de pontos interiores primal-dual e preditor-corretor de barreira logarítmica. O trabalho faz uma avaliação do desempenho computacional dos métodos implementados e do método LINPROG presente no software Matlab® na solução do problema de planejamento da operação em larga escala, para horizontes de cinco e de dez anos. As simulações foram feitas baseados em dados do Plano Decenal de Energia (PDE) 2022 e apresentaram desempenhos satisfatórios. / The operational planning of electric power systems is directly related to the dispatch of hydroelectric and thermal power plants. The Brazilian electric energy park is a predominantly hydraulic system, due to its geographic characteristics. Due to the large size of the electrical systems, the optimization of the hydrothermal dispatch problem is an extremely complex task that can be carried out efficiently, seeking to optimize the operation of the reservoir in the hydroelectric plants aimed at reducing the cost of the necessary thermal generation to meet the load and possible energy deficits, and a high level of security. This work discusses the development and implementation of a software to solve the hydrothermal dispatch problem in three load steps. In this dissertation the hydrothermal dispatching problem is formulated as a linear programming program, which in term is solved by the following methods of interior point: primal-dual and predictor-corrector with logarithmic barrier. This work provides an evaluation of the computational performance of the implemented methods and LINPROG, presents in the software Matlab®, to solve a large scale operational planning problem, for horizons of five and ten years. The simulation were made based on data from the “Plano Decenal de Energia (PDE) 2022” and showed satisfactory performance.

O objetivo deste trabalho consiste no desenvolvimento, estudo e implementação de métodos de pontos interiores específicos para o problema de planejamento do tratamento de câncer por radioterapia. Este é um problema de grande porte que contém uma estrutura matricial particular. A exploração desta estrutura de forma eficiente obtém bom desempenho computacional, através da redução da dimensão dos sistemas lineares que devem ser resolvidos a cada iteração, agilizando a definição de um tratamento adequado, uma vez que tipicamente várias simulações são realizadas antes da definição de um plano definitivo. Resultados numéricos em Matlab ilustram a eficiência desta abordagem em problemas reais e mostram a superioridade do método preditor corretor em comparação ao método primal-dual. / In this work, a specialized interior point method is developed for planning cancer treatment by radiotherapy. This is a large-scale problem with a specific matrix structure. That structure is explored in an efficient way reducing the dimension of the linear system which must be solved at each iteration speeding up the treatment design since usually several versions must be solved to obtain a satisfactory plan. Moreover, the system obtained is sparse, symmetric and positive definite. Numerical results in Matlab illustrate the efficiency of this approach in real problems and show the superiority of the preditor-corrector method in comparison to the primal-dual method.

This thesis aims to study how flat dielectric lenses can be designed. The usage of flat lenses is steadily increasing as they are smaller and less bulky than traditional convex lenses. Instead of a lens with a curved surface the permittivity in the lens is varied to achieve the same effect. Two different computational methods were investigated when approaching this problem: physical and geometrical optics. In physical optics the incoming radio waves are treated as waves in contrast to geometrical optics where it is considered as rays. Both methods are used as approximations of Maxwell's equations. The variation of permittivity in the lens was formulated as an optimisation problem where the lens' focusing abilities were maximised. The optimisation was implemented with an interior point method. Both arbitrary permittivity distributions as well as predetermined distributions were examined in this work. All optimised lens models were then simulated in a full wave commercial simulation software to verify and compare the two. The simulations showed that both approaches gave promising results as they focused the electromagnetic wave in a satisfying way. However the physical optics approach was more prominent as the focused radio waves had a much higher magnitude than the approach based on geometrical optics. The conclusion was therefore that physical optics is the preferred approach.

No description available.

The aim of this thesis is to optimize hydro power plants with data generated from observations and field tests at the plants. The output is optimal production tables and curves in order to operate and plan hydro power plants in an optimized way concerning power output, efficiency and distribution of water. The thesis is performed in collaboration with Vattenfall AB, which currently use an internal optimization program called SEVAP. Two alternative methods have been selected, employed and compared with the current optimization program, these are Interior-Point Method and Sequential Quadratic Programming. Three start-point strategies are created to increase the probability of finding a global optima. A heuristic rule is used for selection of strategy in order to prevent rapid changes in load distribution for small variations in dispatched water. The optimization is performed at three plants in Sweden with different size and setup. The results of this evaluation showed marginally better results for the employed methods in comparison to the currently used optimization. Further, the developed program is more flexible and compatible to integrate with future digitalization projects. / Syftet med detta examensarbete är att optimera vattenkraftverk med data som genererats från indextester vid kraftverken. Resultatet är optimala produktionstabeller och kurvor för drift och planering av vattenkraftverk. Dessa är baserade på att optimalt fördela vattnet mellan aggregaten för att maximera uteffekt och verkningsgrad. Detta arbete har utförts i samarbete med Vattenfall AB, som för närvarande använder ett internt optimeringsprogram som heter SEVAP. Två optimeringsmetoder har valts, implementerats och jämförts med det nuvarande optimeringsprogrammet. Dessa metoder är inrepunktsmetoden (IPM) och sekventiell kvadratiskt programmering (SQP). Tre startpunktsstrategier har används för att öka sannolikheten att hitta ett globalt optima. För att förhindra hastiga förändringar i lastfördelning för små variationer av avsänt vatten har en heuristisk regel används. Optimeringen har utförts på tre stationer med olika uppsättning och storlek. Resultatet av detta examensarbete visar marginellt bättre resultat för de använda metoderna i jämförelse med den nuvarande optimeringen. Det utvecklade programmet är flexibelt och kompatibelt att integrera med framtida digitaliseringsprojekt.

Low-thrust interplanetary spacecraft trajectory optimization poses a uniquely difficult problem to solve because of the inherent nonlinearities of the dynamics and constraints as well as the large size of the search space of possible solutions. Tools currently exist that optimize low-thrust interplanetary trajectories, but these tools are rarely openly available to the public, and when they are available they require multiple interfaces between multiple different packages. The goal of this work is to present a new piece of low-thrust interplanetary spacecraft trajectory optimization software that is open-source and entirely self-contained so that more people can have access to the ability to design interplanetary trajectories. To achieve this goal, a gradient-descent based nonlinear programming method, called the interior point method, was used. The nonlinear programming method was chosen so that results from this work could be compared and contrasted with results from Spacecraft Trajectory Optimization Suite (STOpS), which uses heuristics to iterate towards a solution. Interior point methods are popular because of their ability to handle large amounts of equality and inequality constraints, which is a characteristic that is valuable for low-thrust interplanetary spacecraft trajectories. The software developed, Interior Point Optimizer (IP Optimizer), was then validated against test cases with known solutions to ensure that the software delivered the intended results. Lastly, a constraint satisfaction, a minimum-time, and a maximum-final-mass optimization problem were solved and compared with literature to illustrate the advantages of IP Optimizer and the methods it employs. For the constraint satisfaction problem, IP Optimizer was able to find a solution that exactly satisfied the desired terminal constraints whereas STOpS had an error of 2.29 percent. In this case, IP Optimizer had a reduced runtime of 15 percent compared to STOpS as well. When minimizing time for a spacecraft transfer, IP Optimizer improved upon the solution found by STOpS by 5.3 percent. The speed of convergence for IP Optimizer was almost twice as fast as STOpS for this case. These results show that IP Optimizer is faster than STOpS at converging on a solution and the solution it converges to has a better objective value and more accurately satisfies the terminal constraints than STOpS. Lastly, the maximum-final-mass problem resulted in an objective value that was only 0.5 percent lower than the value found in literature.

<p> This thesis addresses the design of fractionally-spaced equalizers for a digital communication system which is susceptible to Adjacent Channel Interference (ACI). ACI can render an otherwise well designed system prone to excess bit errors. Algorithms for a trained adaptive FIR linear fractionally-spaced equalizer (FSE) with explicit sidelobe control are developed in order to provide robustness to ACI. The explicit sidelobe control is achieved by imposing a quadratic inequality constraint on the frequency response of the equalizer at a discrete set of frequency points in the sidelobe region.</p> <p> Algorithms are developed for both block adaptive and symbol-by-symbol adaptive modes. These algorithms use interior point optimization techniques to find the optimal equalizer coefficients. In the block adaptive mode, the problem is reformulated as a Second Order Cone Program (SOCP). In the symbol-by-symbol adaptive mode, the philosophy of the barrier approach to interior point methods is adopted. The concept of a central path and the Method of Analytic Centers (MAC) are used to develop two practically implementable algorithms, namely IPM2 and SBM, for performing symbol-by-symbol adaptive, fractionally-spaced equalization, with multiple quadratic inequality constraints.</p> <p> The performance of the proposed algorithms is compared to that of the Wiener filter, and the standard RLS algorithm with explicit diagonal loading. In the computer simulations, the proposed algorithms perform better in the sense that they provide the desired robustness when the communication model is prone to intermittent interferers in the sidelobe region of the frequency response of the FSE. Although the proposed algorithms have a moderately higher computational cost, their insensitivity to the deleterious effects of ACI make them an attractive choice in certain applications.</p> / Thesis / Master of Applied Science (MASc)