Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2007. / "May, 2007." Title from electronic thesis title page (viewed 4/28/2009) Advisor, Ali Hajjafar; Faculty readers, Linda Marie Saliga, Lala Krishna; Department Chair, Joseph W. Wilder; Dean of the College, Ronald F. Levant; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

Thesis (Ph.D.)--Memorial University of Newfoundland, 1999. / Bibliography: leaves 173-181.

No description available.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Vita. / Includes bibliographical references. / by Woodrow Whitlow, Jr. / Ph.D.

When integer programming (IP) models are used in operational situations there is a need to consider the tradeoff between the conflicting goals of solution quality and solution time, since for many problems solving realistic-size instances to a tight tolerance is still beyond the capability of state-of-the-art solvers. However, by appropriately defining small instances, good primal solutions frequently can be found quickly. We explore this approach in this thesis by studying the design of algorithms that produce solutions to an integer program by solving restrictions of the problem via integer programming technology. We refer to this type of algorithm as IP-based search and present algorithms for network design problems of both real-world and academic interest. Along with algorithms that exploit the structure of the problem studied we also present a general integer programming algorithm that uses column generation to choose the restrictions to solve.

Thesis (Ph. D.)--Carnegie Mellon University, 2003. / Title from PDF title page (viewed Dec. 18, 2009). Includes bibliographical references (p. 49-52).

Integral equations arise in many scienti c and engineering problems. A large class of initial and boundary value problems can be converted to Volterra or Fredholm integral equations. The potential theory contributed more than any eld to give rise to integral equations. Integral equations also has signi cant application in mathematical physics models, such as di rac- tion problems, scattering in quantum mechanics, conformal mapping and water waves. The Volterra's population growth model, biological species living together, propagation of stocked sh in a new lake, the heat transfer and the heat radiation are among many areas that are described by integral equations. For limited applicability of analytical techniques, the numer- ical solvers often are the only viable alternative. General computational techniques of solving integral equation involve discretization and generates equivalent system of linear equations. In most of the cases the discretization produces dense matrix. Multigrid methods are widely used to solve partial di erential equation. We discuss the multigrid algorithms to solve integral equations and propose usages of distributive relaxation and the Kaczmarz method. / Department of Mathematical Sciences

Dans cette thèse, nous avons étudié les méthodes de régularisation pour la résolution numérique de problèmes avec équilibres. Dans une première partie, nous nous sommes intéressés aux problèmes de complémentarité au travers de deux applications : les équations en valeur absolue et les problèmes de parcimonie. Dans une seconde partie, nous avons étudié les problèmes d'optimisation sous contraintes de .complémentarité. Après avoir définies des conditions d'optimalité pour ces problèmes nous avons proposé une nouvelle méthode de régularisation appelée méthode des papillons. A partir d'une étude de la résolution des sous-problèmes de la régularisation nous avons défini un algorithme avec des propriétés de convergence forte. Tout au long de ce manuscrit nous nous sommes concentrés sur les propriétés théoriques des algorithmes ainsi que sur leurs applications numériques. La dernière partie de ce document est consacrée aux résultats numériques des méthodes de régularisation. / In this thesis, we studied the regularization methods for the numerical resolution of problems with equilibria. In the first part, we focused on the complementarity problems through two applications that are the absolute value equation and the sparse optimization problem. In the second part, we concentrated on optimization problems with complementarity constraints. After studying the optimality conditions of this problem, we proposed a new regularization method, so-called butterfly relaxation. Then, based on an analysis of the regularized sub-problems we defined an algorithm with strong convergence property. Throughout the manuscript, we concentrated on the theoretical properties of the algorithms as well as their numerical applications. In the last part of this document, we presented numerical results using the regularization methods for the mathematical programs with complementarity constraints.

Fu Sau-chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 68-71). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background of Explosion and Implosion Problems --- p.1 / Chapter 1.2 --- Background of the Development of Numerical Schemes --- p.2 / Chapter 1.3 --- Organization of the Thesis --- p.5 / Chapter 2 --- Governing Equations and Numerical Schemes --- p.6 / Chapter 2.1 --- Governing Equations --- p.6 / Chapter 2.2 --- Numerical Schemes --- p.8 / Chapter 2.2.1 --- Splitting Scheme for Partial Differential Equations with Source Terms --- p.8 / Chapter 2.2.2 --- Boundary Conditions --- p.9 / Chapter 2.2.3 --- "Numerical Solvers for the ODEs - The Second-Order, Two-Stage Runge-Kutta Method" --- p.10 / Chapter 2.2.4 --- Numerical Solvers for the Pure Advection Hyperbolic Problem - The Second-Order Relaxed Scheme --- p.11 / Chapter 3 --- Numerical Results --- p.29 / Chapter 3.1 --- Spherical Explosion Problem --- p.30 / Chapter 3.1.1 --- Physical Description --- p.32 / Chapter 3.1.2 --- Comparison with Previous Analytical and Experimental Results --- p.33 / Chapter 3.2 --- Cylindrical Explosion Problem --- p.46 / Chapter 3.2.1 --- Physical Description --- p.46 / Chapter 3.2.2 --- Two-Dimensional Model --- p.49 / Chapter 3.3 --- Spherical Implosion Problem --- p.52 / Chapter 3.3.1 --- Physical Description --- p.52 / Chapter 3.4 --- Cylindrical Implosion Problem --- p.53 / Chapter 3.4.1 --- Physical Description --- p.53 / Chapter 3.4.2 --- Two-Dimensional Model --- p.53 / Chapter 4 --- Conclusion --- p.65 / Bibliography --- p.68

Orientador: Nelson Luis Saldanha da Fonseca / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-19T00:15:10Z (GMT). No. of bitstreams: 1 Silva_PedroHenriqueGomesda_M.pdf: 2438089 bytes, checksum: 1531b4c3213529b3d7064cb49b95e0c8 (MD5) Previous issue date: 2011 / Resumo: A tecnologia de Rádio sobre Fibra (Radio over Fiber - RoF) possibilita o barateamento da instalação e manutenção de redes de acesso sem fio, dado que a distribuição da utilização dos sinais de radiofrequência (RF) pode ser otimizada, bem como emprega-se, nessas redes, antenas mais simples e baratas. Dentre as tecnologias de redes sem fio de acesso banda larga (Broadband Wireless Access - BWA), o padrão IEEE 802.16, conhecido como WiMAX, vem sendo apresentado como uma solução de baixo custo para o acesso última milha à Internet ou como meio de distribuição backhaul. Suas características, muito semelhantes às das redes celulares, tornam interessante o emprego da tecnologia de RoF para a instalação e expansão das redes WiMAX a um baixo custo. Nesta dissertação, apresenta-se um estudo sobre o dimensionamento da tecnologia RoF para redes WiMAX. Apresentam-se medidas de desempenho que levam em consideração os ajustes dos parâmetros de sincronização das camadas física e de controle de acesso ao meio. O objetivo desse estudo é servir de base para o planejamento e instalação dessas redes, levando em consideração restrições devido à degradação de desempenho que a introdução da fibra óptica impõe. Esta dissertação estuda, adicionalmente, o problema de otimização do uso dos recursos de rádio da rede, mais especificamente do posicionamento e alocação das estações base. A proposta considera uma arquitetura de rede sem fio com diversas camadas de antenas, cada camada com células de diferentes raios de cobertura. As células são implantadas através de associações entre as antenas e as estações base disponíveis. Para a otimização da rede, propõe-se um modelo baseado em programação linear inteira que distribui, de maneira ótima, os recursos e encontra a melhor configuração de células para minimizar o número de BSs usadas na rede, para maximizar a receita, ou para obter esses dois critérios simultaneamente. O custo computacional do problema de otimização proposto é bastante alto, o que inviabiliza o seu emprego em redes móveis. Para contornar esse problema, são apresentados também algoritmos rápidos baseados em relaxação linear da programação linear inteira que possibilitam a obtenção de soluções de boa qualidade em tempo reduzido / Abstract: The Radio over Fiber technology allows the reduction of the cost of installation and maintenance of wireless access networks, since it can allow an optimized use of radio frequency (RF). Moreover, it employs simplified and inexpensive antennas. The IEEE 802.16 wireless networks, known as WiMAX, are low cost solutions for the last mile access to the Internet. Its characteristics are very similar to those of cellular networks, which makes attractive the use of RoF technology for the installation and expansion of WiMAX networks at low cost. This dissertation studies the use of RoF technology for WiMAX networks, which considers the parameters of physical layer and medium access synchronization. Results can be used as guideline for planning of these networks. This dissertation also studies the optimization of the use of radio resources of the network, specifically the problem of positioning base stations. The proposed architecture considers a wireless network with several layers of antennas, each layer with cells of different radii of coverage. The cells are deployed dynamically by the association between antennas and the available base stations. It is proposed a network optimization model based on integer linear programming that optimally distributes the radio resources and finds the best configuration to either minimize the number of Base Stations used in the network, or to maximize the operator revenue, as well as ato try to achieve both criteria simultaneously. The computational cost of the proposed optimization problem is quite high, which prevents its use in mobile networks. To circumvent this problem, it is also presented fast algorithms based on linear relaxation of the integer linear programming model, which enable the obtainment of good solutions in short time frames / Mestrado / Ciência da Computação / Mestre em Ciência da Computação