Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using synthetically generated or actually measured scattered fields, show that the images recovered by these sparsity-regularized methods are sharper and more accurate than those produced by existing methods. The methods developed in this work have potential application areas ranging from oil/gas reservoir engineering to biological imaging where sparse domains naturally exist.

The diploma thesis deals with linear integer optimization in production logistics via mathematical programming. This tool is used for optimization of the time production schedule with a number of various jobs performed by a company with limited resources. The thesis solves the problem in conjunction with TOSHULIN, a.s. company, which is interested in solving the problem. As a result is the software implementation in which Gantt chart is created as its output.

Systematic conservation planning is an essential part of biodiversity preservation.

Målet har varit att öka andelen skrotanvändning i omsmältan med hjälp av linjärprogrammering som en optimering vid en aluminiumindustri, vilket uppnåddes. Det har gjorts en nulägesanalys om hur aluminium används, hur produktionen fungerar samt var det faller ut skrot. Följande har en teoretisk referensram upprättats med källor från tidigare problem som lösts med linjärprogrammering, en beskrivning av linjärprogrammering och en matematisk uppställning. Det har också beskrivits hur problemet ställts upp, vilka infallsvinklar som använts och de resultat som optimeringen gett. Det har även gjorts arbete kring den måluppfyllande optimeringen som presenterats efter resultatet, vilket följs av en diskussion och slutsats med rekommendationer för framtida arbete inom ämnet. Optimeringen är gjord både mot volym som målfunktion, vilket ger en ökad användning av skrotet, och med pris som målfunktion, som bidrar till en minskad kapitalbindning i skrotet som finns kvar. Dagslägets användning av skrot uppgår till cirka 30 % per år medan optimeringsmodellen gjord på endast 17 av 72 recept skulle kunna få i så mycket som 90 % av hela årets producerade skrot. En optimering på endast ett recept visar också på att det är möjligt att smälta om och producera gjutlegeringar bestående av hög andel enbart skrot. / The aim with this project was to increase the amount of used scrap in the remelt of aluminum alloys by using linear programming, which was successfully done. A status analysis about the average use and characteristics of aluminum has been described, as well as a mapping of the todays industry within the company. This is followed by a theoretical chapter containing references from previous work solved with linear programming, and a description of LP including the mathematical model. The attempt to solve this problem is carefully shown in the forthcoming chapters together with the different approaches that were used. The results are presented with analysis of each optimization, followed by a discussion and a conclusion including future recommendations. The model is used with two different objective functions to get perspective, volume to maximize the amount of used scrap and price to increase use of high valued alloys in order to decrease capital accumulation within the non-used scrap. The remelt process of today consumes about 30 % of the total scrap produced during one year. This model shows that it is possible, by having 17 out of 72 recipes, to use 90 % of all scrap. One optimization for a single recipe also proved that it is possible to produce an alloy consisting of basically scrap.

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With dynamic spectrum access emerging as an important paradigm for efficient spectrum use, mechanisms are required to ensure disciplined spectrum access by secondary users. This must be done without requiring secondary users to disclose private data, such as their exact usage pattern or identities of parties involved. We formulate, design and evaluate a mechanism to collect spectrum activity information using a set of CPEs. A system design is presented which uses a number of techniques to address mobility and security issues involved in relying on CPEs to collect spectrum activity information. The system imposes an observation probability such that a rational cheater is dissuaded from spectrum misuse. The minimum number of CPEs required to impose this observation probability is determined by formulating it as an integer linear program. The security and privacy of this system is analyzed, along with simulation results to evaluate the quality of the solution. Based on the current design, directions for future work are identified and preliminary approaches are presented. / Master of Science

Made available in DSpace on 2016-08-10T10:40:17Z (GMT). No. of bitstreams: 1 Geovane Reges de Jesus Campos.pdf: 308868 bytes, checksum: 7d7dde587ca6eede4281609bfad2c151 (MD5) Previous issue date: 2012-09-04 / This paper presents a study for the classroom assignment problem for the PUC Goiás, Area 3, Campus I, based on a programming system (SAPA), the Hungarian algorithm, and on the idea of solving the problem time by time. The problem is solved with real data no more than 6 seconds. / Este trabalho apresenta um estudo para o problema de designação de salas de aula para a PUC Goiás, área 3, Campus I, baseado em um sistema de programação (SAPA), no algoritmo Húngaro e na idéia de resolver o problema horário por horário. O problema é resolvido, com dados reais, em não mais do que 6 segundos.

Made available in DSpace on 2016-08-10T10:40:20Z (GMT). No. of bitstreams: 1 JEANCARLO RIBEIRO.pdf: 683766 bytes, checksum: 28e6690b67012436dd91788ec7ff346b (MD5) Previous issue date: 2013-06-17 / The classroom assignment problem at universities consist in distributing classes scheduled for the appropriate rooms, respecting the requirements in each situation. The objective of this work is to apply the Hungarian algorithm and a computational system to solve the classroom assignment problem time by time. The tests were performed with real data from the PUC Goiás for a quantitative of 5116 classes into 313 classrooms. As a result, we solved the problem in approximately 12 minutes and the solution quality was compared with manual designation usually applied by the institution, which takes a month and a half. / O problema de designação de salas de aula em Universidades consiste em distribuir turmas programadas para as devidas salas, respeitando os requisitos estabelecidos em cada situação. O objetivo deste trabalho é a aplicação do algoritmo húngaro e de um sistema computacional para a resolução do problema de alocação horário por horário. Os testes foram realizados com dados reais da PUC Goiás para um quantitativo de 5116 turmas em 313 salas de aula. Como resultados, resolvemos o problema em aproximadamente 12 minutos e comparamos a qualidade da solução com a designação manual usualmente realizada pela Instituição, a qual leva um mês e meio.