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Made available in DSpace on 2014-07-29T15:14:25Z (GMT). No. of bitstreams: 1 Tese Arissane Damaso Fernandes.pdf: 1420009 bytes, checksum: 44799ec735e444621601af89ffb41ed7 (MD5) Previous issue date: 2011-05-06 / Ignácio Rangel played an important role in the consolidation of so-called conditions of capitalist production in Brazil, mainly in the years 1950-1970. As economic adviser of President Getúlio Vargas (between 1952 and 1954), he participated in the elaboration of projects of Petrobras and Eletrobras, he also headed the Economics Department of the BNDES (which at the time, played the role that years later would be of the Ministry of Planning) and participated in the drafting of the Plan of Goals in government of Juscelino Kubitschek. However, he remains unknown by most historians (and academics in general). The intent of this study is precisely to rescue the historical aspect of the theory rangeliana, which, while presenting an interpretation of Brazilian reality had a specific goal: to intervene in reality through analysis that sought effective proposal of action. The central objective of this study is, thus, understand political-institutional performance and the significance of the trajectory of Ignacio Rangel to the history of Brazil. / Ignácio Rangel desempenhou um papel fundamental na consolidação das chamadas condições de produção capitalistas no Brasil, essencialmente nos anos 1950-1970. Como assessor econômico do presidente Getúlio Vargas (entre 1952 e 1954), ele participou da elaboração dos projetos da Petrobrás e da Eletrobrás, ele também chefiou o Departamento de Economia do BNDES (que, na época, desempenhava o papel que, anos depois, caberia ao Ministério do Planejamento ) e participou da elaboração do Plano de Metas, no governo de Juscelino Kubitschek. Entretanto, ele permanece desconhecido por grande parte dos historiadores (e dos acadêmicos de maneira geral). A intenção deste estudo é a de justamente resgatar o aspecto histórico da teoria rangeliana, a qual, ao apresentar uma interpretação da realidade brasileira tinha um objetivo concreto: intervir nessa realidade através de uma análise que buscava proposta efetiva de ação. O objetivo central deste estudo é, portanto, compreender a atuação político-institucional e o significado da trajetória de Ignácio Rangel para a história do Brasil.

The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.