No description available.

O sistema de osseointegração desenvolvido por Branemark revolucionou o campo das reabilitações protéticas, incentivando os profissionais a indicar e realizar próteses do tipo overdentures. Estes dispositivos representam uma ótima alternativa para solucionar os problemas dos pacientes desdentados, insatisfeitos por diversos fatores. Várias são as associações entre os implantes e os sistemas de conexões empregados em overdentures. A literatura e a prática clínica fazem observar que na dependência do sistema de conexão empregado, há uma diferença no comportamento biomecânico, realizado por este conjunto: prótese/implante/conexão. Desta forma, é importante analisar como as tensões se distribuem sobre as estruturas que suportam estas cargas, uma vez que não existe o ligamento periodontal ao redor dos implantes que promove o mecanismo fisiológico, natural nos dentes. Assim, o objetivo desta investigação foi de avaliar, com o auxílio do método fotoelástico, o comportamento da distribuição das tensões em sobredentaduras (overdentures), suportadas por quatro implantes Ankylos®/ Dentsply®, utilizando-se o sistema protético de conexão de coroas cônicas Syncone®/ Dentsply®, onde se comparou duas formas de distribuição dos implantes, na primeira (CPM1) os implantes foram posicionados nas regiões de incisivos centrais e pré-molares e o segundo (CPM2) os implantes estavam posicionados nas regiões de caninos e pré-molares. Os modelos receberam cargas de forma crescente de 0,0 a 9,0 kg e, as tensões resultantes nas estruturas de suporte, foram analisadas fotoelasticamente. De acordo com a metodologia empregada nesta pesquisa, somos levados a concluir que: 1) Quando se associa o sistema Syncone® com overdenture ou sobredentadura, apoiada e retida sobre quatro implantes, sendo 2 localizados na região de incisivos centrais e 2 situados, diametralmente opostos, na região de segundos pré-molares na mandíbula - CPM1 - o rebordo residual é quem recebe a maior quantidade de tensões em relação aos implantes; 2) Quando se associa o sistema Syncone® com overdenture ou sobredentadura, apoiada e retida sobre 4 implantes, dispostos 2 a 2, bilateralmente e diametralmente opostos, nas regiões de caninos e pré-molares, na mandíbula (CPM2), as maiores tensões são transmitidas ao rebordo residual, sendo que os implantes suportes resultam mais preservados; 3) Comparativamente, o CPM2, aparenta ter transmitido menores tensões aos implantes que o CPM1; 4) Os implantes são preservados quanto à ocorrência de uma sobrecarga, durante a máxima intercuspidação dos arcos dentários, quando se emprega o sistema Syncone® associado à overdenture ou sobredentadura. / The osseo-integrated system develop by Branemark has revolutionized the prosthetic rehabilitation field, encourage the professionals to indicate and perform prostheses like overdentures. These devices represent an optimal alternative to solve the full dentures patient?s problems, dissatisfied for diverse factors. There are several associations between implants and prosthetic connectors employees for overdentures. The literature and the clinic practice may observe that according of the connection system employed, there is a difference into the biomechanical behavior, realized for this set: prostheses/implant/connection. From this forms, it is important to analyze how the tensions are distributing on the structures subject that support these loads, since it doesn\'t exist the periodontal ligament around the implants, what promotes the physiological mechanism of the natural teeth. Such, the purpose from this investigation was appraising, with the aid of the photoelastic method, the distribution way from the tensions at the overdentures, supported by four implants Ankylos®/ Dentsply, by using the prosthetic system of connection of conic crowns ? Syncone®/ Dentsply, were applied loads from 0,0 to 9,0kg, in crescent forms and, the tensions resulting on the support structures, have been analyzed by the photoelasthic method. Where two forms of distribution of the implantations were compared, first (CPM1) the implants were located at the regions of the central incisors and pre-molar, and as (CPM2) the implants were located at the regions of canines and pre-molar. The models had received loads of increasing form, from 0,0 to 9,0 kg and, the resultant tensions in the support structures, had been analyzed by the photoelastic method. In agreement with the methodology used in this research, we are led to conclude that: 1) When the overdenture is associated with Syncone® system, supported and retained by 4 implants, being 2 located in the region of central incisors and 2, diametrical opposing ones, in the region of the second pre-molar (CPM1) the residual alveolar ridge is who receives the biggest amount of tensions in relation to the implants; 2) When the overdenture is associated with Syncone® system, supported and retained by 4 implants, bilaterally and diametrical opposing ones, in the regions of canine and pre molar (CPM2), the biggest tensions were transmitted to the residual alveolar ridge, being the implants supports resulted more preserved; 3) Comparatively, the CPM2, seems to have transmitted less tensions to the implants than the CPM1; 4) The implants were preserved as the occurrence of an overload, during the maximum intercuspidação of the dental arcs, when the overdenture associated with Syncone® system has been used.

Neste trabalho abordaremos alguns assuntos relacionados Ãs SeÃÃes CÃnicas: elipse, parÃbola e hipÃrbole. O trabalho està dividido em cinco capÃtulos: IntroduÃÃo; Origem das CÃnicas; EquaÃÃes das CÃnicas; Propriedades de ReflexÃo das CÃnicas; Construindo CÃnicas. No segundo capÃtulo, falaremos sobre o problema da duplicaÃÃo do cubo que, segundo a HistÃria da MatemÃtica, deu origem as cÃnicas e citaremos alguns matemÃticos cujos trabalhos contribuÃram para o desenvolvimento do estudo dessas curvas. No terceiro capÃtulo, estudaremos as equaÃÃes cartesianas das cÃnicas, bem como as suas representaÃÃes grÃficas e os principais elementos da cada cÃnica. No quarto capÃtulo, apresentaremos as propriedades de reflexÃo das cÃnicas e algumas aplicaÃÃes muito interessantes dessas propriedades. No Ãltimo capÃtulo, demonstraremos alguns mÃtodos para construir cÃnicas e em seguida faremos essas construÃÃes na prÃtica atravÃs de materiais concretos e por meio de um programa de Geometria DinÃmica, chamado Geogebra. / In this paper we discuss some issues related to Conic Sections: ellipse, parabola and hyperbole. The work is divided into five chapters: Introduction; Origin of Conic Sections; Equations of Conic Sections; Reflection Properties of Conic Sections; Building Conic Sections. In the second chapter, weâll talk about doubling the cube problem that, according to the History of Mathematics, originated the conic sections and talk about some mathematicians whose work contributed to the study of these curves. In the third chapter, we will study the Cartesian equations of conic sections, as well as their graphical representations and the main elements of each curve. In the fourth chapter, we presented the reflection properties of conic sections and some very interesting applications of these properties. In the last chapter, we will show some methods to construct conic sections and then we will make these constructs in practice through concrete materials and through a dynamic geometry program, called Geogebra.

In this thesis, we study and use Conic Quadratic Programming (CQP) for purposes of operational research, especially, for quality improvement in manufacturing. In previous works, the importance and benefit of CQP in this area became already demonstrated. There, the complexity of the regression method Multivariate Adaptive Regression Spline (MARS), which especially means sensitivity with respect to noise in the data, became penalized in the form of so-called Tikhonov regularization, which became expressed and studied as a CQP problem. This was leading to the new method CMARS / it is more model-based and employs continuous, actually, well-structured convex optimization which enables the use of Interior Point Methods and their codes such as MOSEK. In this study, we are generalizing the regression problem by including uncertainty in the model, especially, in the input data, too. CMARS, recently developed as an alternative method to MARS, is powerful in overcoming complex and heterogeneous data. However, for MARS and CMARS method, data are assumed to contain fixed variables. In fact, data include noise in both output and input variables. Consequently, optimization problem&rsquo / s solutions can show a remarkable sensitivity to perturbations in the parameters of the problem. In this study, we include the existence of uncertainty in the future scenarios into CMARS and robustify it with robust optimization which is dealt with data uncertainty. That kind of optimization was introduced by Aharon Ben-Tal and Arkadi Nemirovski, and used by Laurent El Ghaoui in the area of data mining. It incorporates various kinds of noise and perturbations into the programming problem. This robustification of CQP with robust optimization is compared with previous contributions that based on Tikhonov regularization, and with the traditional MARS method.

O sistema de osseointegração desenvolvido por Branemark revolucionou o campo das reabilitações protéticas, incentivando os profissionais a indicar e realizar próteses do tipo overdentures. Estes dispositivos representam uma ótima alternativa para solucionar os problemas dos pacientes desdentados, insatisfeitos por diversos fatores. Várias são as associações entre os implantes e os sistemas de conexões empregados em overdentures. A literatura e a prática clínica fazem observar que na dependência do sistema de conexão empregado, há uma diferença no comportamento biomecânico, realizado por este conjunto: prótese/implante/conexão. Desta forma, é importante analisar como as tensões se distribuem sobre as estruturas que suportam estas cargas, uma vez que não existe o ligamento periodontal ao redor dos implantes que promove o mecanismo fisiológico, natural nos dentes. Assim, o objetivo desta investigação foi de avaliar, com o auxílio do método fotoelástico, o comportamento da distribuição das tensões em sobredentaduras (overdentures), suportadas por quatro implantes Ankylos®/ Dentsply®, utilizando-se o sistema protético de conexão de coroas cônicas Syncone®/ Dentsply®, onde se comparou duas formas de distribuição dos implantes, na primeira (CPM1) os implantes foram posicionados nas regiões de incisivos centrais e pré-molares e o segundo (CPM2) os implantes estavam posicionados nas regiões de caninos e pré-molares. Os modelos receberam cargas de forma crescente de 0,0 a 9,0 kg e, as tensões resultantes nas estruturas de suporte, foram analisadas fotoelasticamente. De acordo com a metodologia empregada nesta pesquisa, somos levados a concluir que: 1) Quando se associa o sistema Syncone® com overdenture ou sobredentadura, apoiada e retida sobre quatro implantes, sendo 2 localizados na região de incisivos centrais e 2 situados, diametralmente opostos, na região de segundos pré-molares na mandíbula - CPM1 - o rebordo residual é quem recebe a maior quantidade de tensões em relação aos implantes; 2) Quando se associa o sistema Syncone® com overdenture ou sobredentadura, apoiada e retida sobre 4 implantes, dispostos 2 a 2, bilateralmente e diametralmente opostos, nas regiões de caninos e pré-molares, na mandíbula (CPM2), as maiores tensões são transmitidas ao rebordo residual, sendo que os implantes suportes resultam mais preservados; 3) Comparativamente, o CPM2, aparenta ter transmitido menores tensões aos implantes que o CPM1; 4) Os implantes são preservados quanto à ocorrência de uma sobrecarga, durante a máxima intercuspidação dos arcos dentários, quando se emprega o sistema Syncone® associado à overdenture ou sobredentadura. / The osseo-integrated system develop by Branemark has revolutionized the prosthetic rehabilitation field, encourage the professionals to indicate and perform prostheses like overdentures. These devices represent an optimal alternative to solve the full dentures patient?s problems, dissatisfied for diverse factors. There are several associations between implants and prosthetic connectors employees for overdentures. The literature and the clinic practice may observe that according of the connection system employed, there is a difference into the biomechanical behavior, realized for this set: prostheses/implant/connection. From this forms, it is important to analyze how the tensions are distributing on the structures subject that support these loads, since it doesn\'t exist the periodontal ligament around the implants, what promotes the physiological mechanism of the natural teeth. Such, the purpose from this investigation was appraising, with the aid of the photoelastic method, the distribution way from the tensions at the overdentures, supported by four implants Ankylos®/ Dentsply, by using the prosthetic system of connection of conic crowns ? Syncone®/ Dentsply, were applied loads from 0,0 to 9,0kg, in crescent forms and, the tensions resulting on the support structures, have been analyzed by the photoelasthic method. Where two forms of distribution of the implantations were compared, first (CPM1) the implants were located at the regions of the central incisors and pre-molar, and as (CPM2) the implants were located at the regions of canines and pre-molar. The models had received loads of increasing form, from 0,0 to 9,0 kg and, the resultant tensions in the support structures, had been analyzed by the photoelastic method. In agreement with the methodology used in this research, we are led to conclude that: 1) When the overdenture is associated with Syncone® system, supported and retained by 4 implants, being 2 located in the region of central incisors and 2, diametrical opposing ones, in the region of the second pre-molar (CPM1) the residual alveolar ridge is who receives the biggest amount of tensions in relation to the implants; 2) When the overdenture is associated with Syncone® system, supported and retained by 4 implants, bilaterally and diametrical opposing ones, in the regions of canine and pre molar (CPM2), the biggest tensions were transmitted to the residual alveolar ridge, being the implants supports resulted more preserved; 3) Comparatively, the CPM2, seems to have transmitted less tensions to the implants than the CPM1; 4) The implants were preserved as the occurrence of an overload, during the maximum intercuspidação of the dental arcs, when the overdenture associated with Syncone® system has been used.

No description available.

With the rapidly growing need for long-term decision making in the presence of stochastic future events, it is important to devise novel mathematical optimization tools and develop computationally efficient solution approaches for solving them. Two-stage stochastic programming is one of the powerful modeling tools that allows probabilistic data parameters in mixed integer programming, a well-known tool for optimization modeling with deterministic input data. However, akin to the mixed integer programs, these stochastic models are theoretically intractable and computationally challenging to solve because of the presence of integer variables. This dissertation focuses on theory, algorithms and applications of two-stage stochastic mixed integer (non)linear programs and it has three-pronged plan. In the first direction, we study two-stage stochastic p-order conic mixed integer programs (TSS-CMIPs) with p-order conic terms in the second-stage objectives. We develop so called scenario-based (non)linear cuts which are added to the deterministic equivalent of TSS-CMIPs (a large-scale deterministic conic mixed integer program). We provide conditions under which these cuts are sufficient to relax the integrality restrictions on the second-stage integer variables without impacting the integrality of the optimal solution of the TSS-CMIP. We also introduce a multi-module capacitated stochastic facility location problem and TSS-CMIPs with structured CMIPs in the second stage to demonstrate the significance of the foregoing results for solving these problems. In the second direction, we propose risk-neutral and risk-averse two-stage stochastic mixed integer linear programs for load shed recovery with uncertain renewable generation and demand. The models are implemented using a scenario-based approach where the objective is to maximize load shed recovery in the bulk transmission network by switching transmission lines and performing other corrective actions (e.g. generator re-dispatch) after the topology is modified. Experiments highlight how the proposed approach can serve as an offline contingency analysis tool, and how this method aids self-healing by recovering more load shedding. In the third direction, we develop a dual decomposition approach for solving two-stage stochastic quadratically constrained quadratic mixed integer programs. We also create a new module for an open-source package DSP (Decomposition for Structured Programming) to solve this problem. We evaluate the effectiveness of this module and our approach by solving a stochastic quadratic facility location problem. / Doctor of Philosophy / With the rapidly growing need for long-term decision making in the presence of stochastic future events, it is important to devise novel mathematical optimization tools and develop computationally efficient solution approaches for solving them. Two-stage stochastic programming is one of the powerful modeling tools that allows two-stages of decision making where the first-stage strategic decisions (such as deciding the locations of facilities or topology of a power transmission network) are taken before the realization of uncertainty, and the second-stage operational decisions (such as transportation decisions between customers and facilities or power flow in the transmission network) are taken in response to the first-stage decision and a realization of the uncertain (demand) data. This modeling tool is gaining wide acceptance because of its applications in healthcare, power systems, wildfire planning, logistics, and chemical industries, among others. Though intriguing, two-stage stochastic programs are computationally challenging. Therefore, it is crucial to develop theoretical results and computationally efficient algorithms, so that these models for real-world applied problems can be solved in a realistic time frame. In this dissertation, we consider two-stage stochastic mixed integer (non)linear programs, provide theoretical and algorithmic results for them, and introduce their applications in logistics and power systems. First, we consider a two-stage stochastic mixed integer program with p-order conic terms in the objective that has applications in facility location problem, power system, portfolio optimization, and many more. We provide a so-called second-stage convexification technique which greatly reduces the computational time to solve a facility location problem, in comparison to solving it directly with a state-of-the-art solver, CPLEX, with its default settings. Second, we introduce risk-averse and risk-neutral two-stage stochastic models to deal with uncertainties in power systems, as well as the risk preference of decision makers. We leverage the inherent flexibility of the bulk transmission network through the systematic switching of transmission lines in/out of service while accounting for uncertainty in generation and demand during an emergency. We provide abundant computational experiments to quantify our proposed models, and justify how the proposed approach can serve as an offline contingency analysis tool. Third, we develop a new solution approach for two-stage stochastic mixed integer programs with quadratic terms in the objective function and constraints and implement it as a new module for an open-source package DSP We perform computational experiments on a stochastic quadratic facility location problem to evaluate the performance of this module.

Made available in DSpace on 2016-04-27T16:57:12Z (GMT). No. of bitstreams: 1 Marcelo Balduino Silva.pdf: 31298472 bytes, checksum: 7bddc51f9065f44543df030615d071b0 (MD5) Previous issue date: 2011-11-21 / Secretaria da Educação do Estado de São Paulo / The present dissertation proposes, based on the Mathematics curriculum of São Paulo State Educational Secretary (SEE-SP), complementary activities to the material supplied by the SEE-SP, seeking to approach less discussed aspects of the curriculum on the conic sections.The activities were elaborated according to the instruction to the material designated to the teachers for the use of digital technologies and software of dynamic geometry. Such activities were presented to the state public network teachers, in a formation course offeredby the conic section classes. During the course for the teachers formation audio records were taken of the spontaneous manifestations of the educators.Such manifestations were analyzed in order to answer the following questions: what activities could be recommended for the teacher work based on the São Paulo State curriculum? Which aspects should be taken in consideration by the public network teachers of São Paulo Statefacing the challenge of creating complementary activities to the pedagogical proposal in the teacher sguide book? The records of the teachers manifestations show the importance of continuing formations, the interest for certain approaches and possible obstacles for the implementation of such activities in the classroom / A presente dissertação propõe, baseada no currículo de Matemática do Estado de São Paulo, atividades complementares ao material fornecido pela Secretaria de Educação do Estado de São Paulo SEE-SP procurando abordar aspectos menos discutidos pelo currículo sobre as secções cônicas. As atividades foram elaboradas seguindo a orientação do material destinado aos professores para o uso de tecnologia digital e softwares de matemática dinâmica. Tais atividades foram apresentadas a professores da rede pública estadual, em curso de formação fornecido pela Pontifícia Universidade Católica de São Paulo no primeiro semestre de 2011, no qual o pesquisador foi responsável pelas aulas sobre secções cônicas. Durante o curso de formação dos professores, foram registradas em gravações de áudio, as manifestações espontâneas dos educadores. Tais manifestações foram analisadas a fim de responder as seguintes questões: Que atividades poderiam ser recomendadas para o trabalho do professor com base no currículo atual do Estado de São Paulo? Quais aspectos seriam levados em conta pelos professores da rede pública do Estado de São Paulo diante do desafio de criar atividades complementares à proposta pedagógica do caderno do professor? Os registros das manifestações dos professores mostram a importância da formação continuada, o interesse por determinadas abordagens e possíveis obstáculos na implantação em sala de aula destas atividades

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-22T13:24:09Z No. of bitstreams: 2 Nogueira, Leonardo Bernardes.pdf: 4758026 bytes, checksum: 81be665ec243b277cb285cc686730f04 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-23T11:17:17Z (GMT) No. of bitstreams: 2 Nogueira, Leonardo Bernardes.pdf: 4758026 bytes, checksum: 81be665ec243b277cb285cc686730f04 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-09-23T11:17:17Z (GMT). No. of bitstreams: 2 Nogueira, Leonardo Bernardes.pdf: 4758026 bytes, checksum: 81be665ec243b277cb285cc686730f04 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-03-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This paper begins with a brief history about the development of vector spaces and linear transformations, then presents fundamental concepts for the study of Linear Algebra, with greater focus on linear operators in the R2 space. Through examples it explores a wide range of operators in R2 in order to show other applications of matrices in high school and prepares the ground for the presentation a version of Spectral Theorem for selfadjoint operators in R2, which says that for every operator self-adjoint T : E!E in finite dimensional vector space with inner product, exists an orthonormal basis fu1; : : : ;ung E formed by eigenvectors of T, and culminates with their applications on the study of conic sections, quadratic forms and equations of second degree in x and y; on the study of operators associated to quadratic forms, a version of Spectral Theorem could be called as The Main Axis Theorem albeit this nomenclature is not used in this paper. Thereby summarizing a study made by Lagrange in "Recherche d’arithmétique ", between 1773 and 1775, which he studied the property of numbers that are the sum of two squares. Thus he was led to study the effects of linear transformation with integer coefficients in a quadratic form in two variables. / Este trabalho inicia-se com um breve embasamento histórico sobre o desenvolvimento de espaços vetoriais e transformações lineares. Em seguida, apresenta conceitos fundamentais básicos, que formam uma linguagem mínima necessária para falar sobre Álgebra Linear, com enfoque maior nos operadores lineares do plano R2. Através de exemplos, explora-se um vasto conjunto de transformações no plano a fim de mostrar outras aplicações de matrizes no ensino médio e prepara o terreno para a apresentação do Teorema Espectral para operadores auto-adjuntos de R2. Este Teorema diz que para todo operador auto-adjunto T : E!E, num espaço vetorial de dimensão finita, munido de produto interno, existe uma base ortonormal fu1; : : : ;ung E formada por autovetores de T. O trabalho culmina com aplicações sobre o estudo das secções cônicas, formas quadráticas e equações do segundo grau em x e y, no qual o Teorema Espectral se traduz como Teorema dos Eixos Principais, embora essa nomenclatura não seja usada nesse trabalho (para um estudo mais aprofundado neste tema ver [3], [4], [5], [7]). Retomando assim um estudo feito por Joseph Louis Lagrange em "Recherche d’Arithmétique", entre 1773 e 1775, no qual estudou a propriedade de números que são a soma de dois quadrados. Assim, foi levado a estudar os efeitos das transformações lineares com coeficientes inteiros numa forma quadrática de duas variáveis.

In practice, the presence of uncertain parameters in optimization problems introduces new challenges in modeling and solvability to operations research. There are three main paradigms proposed for optimization problems under uncertainty. These include stochastic programming, robust optimization, and sensitivity analysis. In this thesis, we examine, improve, and combine the latter two paradigms in several relevant models and applications. In the second chapter, we study a two-stage adjustable robust linear optimization problem in which the right-hand sides are uncertain and belong to a compact, convex, and tractable uncertainty set. Under standard and simple assumptions, we reformulate the two-stage problem as a copositive optimization program, which in turns leads to a class of tractable semidefinite-based approximations that are at least as strong as the affine policy, which is a well studied tractable approximation in the literature. We examine our approach over several examples from the literature and the results demonstrate that our tractable approximations significantly improve the affine policy. In particular, our approach recovers the optimal values of a class of instances of increasing size for which the affine policy admits an arbitrary large gap. In the third chapter, we leverage the concept of robust optimization to conduct sensitivity analysis of the optimal value of linear programming (LP). In particular, we propose a framework for sensitivity analysis of LP problems, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact, convex, and tractable uncertainty set. This framework unifies and extends multiple approaches for LP sensitivity analysis in the literature and has close ties to worst-case LP and two-stage adjustable linear programming. We define the best-case and worst-case LP optimal values over the uncertainty set. As the concept aligns well with the general spirit of robust optimization, we denote our approach as robust sensitivity analysis. While the best-case and worst-case optimal values are difficult to compute in general, we prove that they equal the optimal values of two separate, but related, copositive programs. We then develop tight, tractable conic relaxations to provide bounds on the best-case and worst case optimal values, respectively. We also develop techniques to assess the quality of the bounds, and we validate our approach computationally on several examples from—and inspired by—the literature. We find that the bounds are very strong in practice and, in particular, are at least as strong as known results for specific cases from the literature. In the fourth chapter of this thesis, we study the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent samples can be observed. Using the Wasserstein metric, we construct an ambiguity set centered at the empirical distribution from the observed samples and containing all distributions that could have generated the observed samples with a high confidence. The problem of interest is to investigate the bound on the expected optimal value over the Wasserstein ambiguity set. Under standard assumptions, we reformulate the problem into a copositive programming problem, which naturally leads to a tractable semidefinite-based approximation. We compare our approach with a moment-based approach from the literature for two applications. The numerical results illustrate the effectiveness of our approach. Finally, we conclude the thesis with remarks on some interesting open questions in the field of optimization under uncertainty. In particular, we point out that some interesting topics that can be potentially studied by copositive programming techniques.