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No. of bitstreams: 8 Dissertação - Kennia Dias Lino - 2014 (1).pdf: 17501266 bytes, checksum: 5327362697ffa1b83fe24ec02465714a (MD5) Dissertação - Kennia Dias Lino - 2014 (2).pdf: 17750722 bytes, checksum: ddd15d700eaddc47e7926ae8ea7054c4 (MD5) Dissertação - Kennia Dias Lino - 2014 (3).pdf: 17312442 bytes, checksum: 945f5927506ef5a70bfcf9112a87b43e (MD5) Dissertação - Kennia Dias Lino - 2014 (4).pdf: 17206304 bytes, checksum: 99a583cd636d3007b0ce37daed02cd21 (MD5) Dissertação - Kennia Dias Lino - 2014 (5).pdf: 17680703 bytes, checksum: f5fdbed901258bf8e5f566b23dc0f5cb (MD5) Dissertação - Kennia Dias Lino - 2014 (6).pdf: 17462888 bytes, checksum: 553e345d448cbf7ef56aee567dfd3b76 (MD5) Dissertação - Kennia Dias Lino - 2014 (7).pdf: 6649928 bytes, checksum: ce7deea9d0a246d55f96e8b54cd936e9 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-06-23 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / : This study 's purpose is to secure tenure and land conflicts in Amazonia from a legal perspective. The discussion of the present work is guided by the question of understanding the Agrarian Law on the regularization performed in the Amazon made by the federal government from the 1960s to the year 2012. For this analysis, this issue will be confronted with agrarian conflicts in a specific area of the Amazon: the Araguaia Northern Mato Grosso. On theoretical grounds the studies of Charles Frederick Tide are used to analyze the concept of property possession and present policies of regularization and José de Souza Martins for understanding the relationship man/weather/land border situation, as is the case North Araguaia Mato Grosso. The methodology of this study is to understand the legal phenomenon, land use regulation in a broader social environment that is the agrarian conflict, by means of literature with analysis of legislation and qualitative data. Thus, initially, it approaches the institute of public lands, the settlement pattern of these and their importance within the regularization. Furthermore, we present an analysis of the laws of regularization in the Amazon permeating this subject by land problem in this region by the military dictatorship government of Fernando Henrique Cardoso. Finally, it examines the regularization relating it to the laws of the Lula government and agrarian conflicts. / Este estudo tem por objeto a regularização fundiária e os conflitos agrários na Amazônia legal a partir de uma perspectiva jurídica. O debate do presente trabalho norteia-se pela questão da compreensão do Direito Agrário sobre a regularização fundiária realizada na Amazônia Legal realizada pelo governo federal a partir da década de 1960 até o ano de 2012. Para tal análise, confrontar-se-á esse tema com os conflitos agrários em uma área específica da Amazônia Legal: o Norte Araguaia Mato-grossense. Na fundamentação teórica utilizam-se os estudos de Carlos Frederico Marés para analisar o conceito de posse e propriedade presentes nas políticas de regularização fundiária e José de Souza Martins para a compreensão da relação homem/tempo/terra em situação de fronteira, como é o caso do Norte Araguaia Mato-grossense. A metodologia deste estudo consiste na compreensão do fenômeno jurídico, a regularização fundiária, em um ambiente social mais amplo que é o conflito agrário, por meio de pesquisa bibliográfica com análise da legislação e qualitativas dos dados. Dessa maneira, inicialmente, aborda-se o instituto das terras devolutas, a forma de ocupação destas e sua importância dentro da regularização fundiária. Além disso, apresenta-se uma análise sobre as leis de regularização fundiária na Amazônia Legal perpassando esse tema pelo problema fundiário nessa região da Ditadura Militar até o governo de Fernando Henrique Cardoso. E por fim, examina-se a regularização fundiária relacionando-a com as leis do governo Lula e os conflitos agrários.

A tomografia por sensoriamento térmico é muito utilizada em diferentes aplicações industriais, tais como a determinação de propriedades térmicas de novos materiais, o controle da produção de calor e a temperatura no processo de manufatura. Entretanto, o emprego de técnicas tomográficas em processos industriais envolvendo transferência de calor ainda carece de métodos robustos e computacionalmente eficientes. Nesse contexto, o principal objetivo deste trabalho é contribuir para o desenvolvimento de uma técnica não intrusiva de medição do coeficiente de convecção a partir de medidas externas de temperatura e fluxo de calor baseada na solução do problema térmico inverso. Para tanto é necessário resolver um problema de condução acoplado a um problema de convecção de calor. Este acoplamento ocorre através do coeficiente de convecção no interior do domínio do problema, cuja determinação pode ser feita através da aplicação de um fluxo de calor e medição das temperaturas resultantes na superfície externa. A tomografia térmica é tratada como um problema de minimização global, cuja função objetivo é um funcional de erro que quantifica a diferença entre as medidas externas não intrusivas (temperatura real) e as medidas calculadas no modelo numérico (temperatura aproximada). A natureza mal condicionada do problema assim formulado se manifesta na superfície de minimização por produzir topologias problemáticas tais como múltiplos mínimos locais, pontos de sela, vales ao redor da solução, platôs, etc. Desse modo, uma técnica bastante sofisticada, capaz de convergir para a solução correta mesmo na presença dessas patologias é necessária para obtenção da solução. Neste trabalho optou-se pelo método de Newton para a minimização deste funcional em que a inversa da matriz Hessiana é substituída por uma pseudo-inversa construída a partir da técnica de Decomposição em Valores Singulares Truncados. Os resultados mostram que a técnica proposta foi capaz de superar os problemas de convergência associados à natureza intrínseca mal condicionada do problema inverso e o coeficiente de convecção foi reconstruído com precisão razoável. / Tomography by thermal sensing is widely used in different industrial applications, such as the determination of thermal properties of new materials, the control of heat production and the temperature in manufacturing processes. However, the application of tomographic techniques in industrial processes involving heat transfer still lacks robust and computationally efficient methods. In this context, the main objective of this thesis is to contribute to the development of a non-intrusive technique for measuring of the convection coefficient from external temperature and heat flow measurements based on the solution of the inverse thermal problem. This requires solving a conduction problem coupled with a heat convection problem, which is coupled through an internal convection coefficient, determined by applying a heat flux and measuring the resulting temperatures on the external boundary. The thermal tomography is treated as a global minimization problem in which the fitness function is an error functional that quantifies the difference between non-intrusive external measurements (actual temperature) and measurements calculated in a numerical model (approximate temperature). The ill-conditioned nature of the problem manifests itself in the minimization problem for producing problematic topologies, such as multiple local minima, saddle points, valleys around the solution, plateaus, etc. Thus, a very sophisticated technique that can converge to the correct solution even in the presence of these pathologies is necessary to obtain the solution. In this thesis the Newton\'s method was used for the minimization of this functional in which the inverse Hessian matrix was replaced by a pseudo-inverse built from the truncated singular value decomposition technique. Results show that the proposed technique was capable of overcoming the convergence problems associated with the intrinsic ill-conditioned nature of the inverse problem and the convection coefficient was reconstructed within reasonable precision.

No início do século XXI as mudanças oriundas das recentes determinações da economia sobre os níveis do político e social adquirem novos conteúdos, especialmente para o Brasil. É neste momento que muitas das reivindicações dos movimentos sociais urbanos, atrelados ao Fórum da Reforma Urbana, transformam-se em políticas públicas, principalmente, a partir da constituição do Ministério das Cidades em 2003. Esta realidade posta em tela traz consigo o desafio de refletir sobre o significado destas mudanças, sobretudo, no contexto do processo de urbanização contemporânea. Na pesquisa que desenvolvemos, procuramos refletir sobre como uma das reivindicações centrais das organizações populares segurança da posse da terra - se torna uma política pública nesse contexto. A segurança da posse da terra é um dos marcos reivindicativos dos movimentos sociais e está ligada ao direito à moradia dos favelados, além de ser um dos instrumentos mais contundentes para resistir às reiteradas expulsões de moradores, muitas vezes empreendidas pelo Estado. No entanto, na passagem da reivindicação da posse para a regularização fundiária de interesse social, há a produção de contradições espaciais vistas por muitos como limites da própria política. São as contradições entre uso/troca e apropriação/dominação do espaço. Uma série de pesquisadores que se debruçam sobre o tema diz que estas contradições são limites e decorrem de um equívoco do planejamento e gestão da cidade. Todavia, partimos da hipótese de que estas contradições espaciais advêm da lógica hegemônica da produção do espaço capitalista e que se conflita com os espaçostempos dos moradores que resistem às estratégias de expropriação. Nessa orientação, consideramos que a produção capitalista do espaço urbano nega a possibilidade de uso dos espaços-tempos garantidores da existência humana, pois estão subsumidos a existência da propriedade privada. Numa sociedade de classes fundada pela desigualdade e a diferenciação, a condição primeira da realização da vida coloca para uma classe a impossibilidade da existência a não ser por uma luta constante - primeiro pelo acesso à moradia como transgressão à propriedade - como a ocupação de lugares da cidade aonde se constroem as moradias - e em segundo lugar pela manutenção desta moradia. Para compreender alguns dos conteúdos das contradições espaciais, tratamos de construir um raciocínio que buscasse entender a produção de três lugares (favelas) na cidade de São Paulo envolvidos no programa de regularização fundiária de interesse social em áreas públicas. Foram selecionadas as favelas Nova Guarapiranga (Capela do Socorro), Abatia (Itaim Paulista) e Maria Cursi (São Mateus). Como método de exposição, alicerçamos o movimento da reflexão sobre uma tríade segregação socioespacial-resistência-apropriação do espaço. Essa tríade representa a articulação contraditória de processos e nos concede a possibilidade de, ao tratarmos algumas das contradições atuais da produção do espaço urbano de São Paulo, vislumbrarmos apontamentos para pensar sobre o direito à cidade. / In the beginning of the 21st century, social and political changes stemming from economic determinations take on new meanings, especially in Brazil. It is in this context that many of the demands put forward by urban social movements, linked to the urban reform agenda, have turned into public policies, especially after the inauguration of the Ministry of Cities in 2003. This reality poses the challenge of thinking about the meaning of these changes for present day urbanization. In our research, we have considered how one of the key demands of political organizations the security provided by tenure has become a public policy. The security provided by land tenure is at the forefront of the demands made by social movements and is attached to the right to housing for slum dwellers. It is also a crucial instrument for resisting efforts often by the state to remove slums and its inhabitants. However, in the transition from a demand of tenure to the regularization of slum occupation, contradictions emerge and many see these as placing serious limitations to these policies. A host of scholars that have studied this issue claim that these limitations stem from planning and management mistakes. Instead, we put forward the hypothesis that these spatial contradictions result from the hegemonic logic associated with capitalist production of space. This logic ends up clashing with the space-time of dwellers who resist strategies of displacement. In order to understand some of the contents of these spatial contradictions, we have brought into focus the production of three places (slums) in Sao Paulo that are part of the program of slum regularization in public land. We have thus selected the slums of Nova Guarapiranga (district of Capela do Socorro), Abatia (district of Itaim Paulista) and Maria Cursi (district of Sao Mateus). As a method of exposition, we have founded our understanding on a triad: sociospatial segregation-resistance-appropriation of space. This triad expresses a contradictory articulation of processes and, in the analysis of some of the contradictions in the production of urban space, it has offered us the possibility of opening up a path to think about the right to the city.

Le schéma de régularisation de Taylor-Lagrange (TLRS) est basé sur la définition des champs en tant que distributions à valeurs d'opérateurs (OPVD). L'expression de ces OPVD implique des fonctions test qui, grâce à leurs propriétés (propriétés d'échelles, super-régularité), permettent d'étendre des distributions singulières à tout l'espace. Ce type de régularisation, que l'on peut qualifier de coupure ultra-douce, est efficace quelque soit le degré de divergence originel et produit des amplitudes finies dépendant d'une échelle intrinsèque sans dimensions. Enfin, ce schéma préserve les symétries du groupe de Poincaré et l'invariance de jauge. Après avoir présenté le formalisme TLRS, celui-ci est appliqué au calcul des corrections radiatives en QED ainsi qu'à celles à la masse du boson de Higgs dans le cadre du modèle standard de la physique des particules. Dans une dernière partie, il est appliqué au modèle de Yukawa dans le cadre de la dynamique sur le front de lumière. Les corrections radiatives et un calcul non-perturbatif d'états liés sont effectués. Ces exemples permettent de vérifier, d'une part, l'applicabilité de ce schéma dans différents cas, et d'autre part, de tester son respect des propriétés de symétrie des théories. / The Taylor-Lagrange regularization scheme (TLRS) is based on the definition of fields as operator valued distributions (OPVD). The expression of these OPVDs implies test functions which, thanks to their properties (scaling properties, super-regularity), allow to extend singular distributions to the whole space. This type of regularization, which could be qualified as an ultra-soft cut-off, is efficient for any order of divergences and produces finite amplitudes depending on an intrinsic dimensionless scale. Finally, this scheme respects the Poincaré group symmetries as well as gauge invariance. After an introduction to the TLRS, it is applied to the calculation of radiative corrections to QED and to the mass of the Higgs boson within the standard model of particle physics. In a last section, it is applied to the Yukawa model using the framework of light front dynamics. Radiative corrections and non-perturbative bound state are calculated. This examples allow to verify, on one hand, the applicability of the TLRS, and on the other hand to test its respect of the symmetry properties of the theories.

Ill-posed inverse problems with quadratic structure are introduced, studied and solved. As an example an inverse problem appearing in laser optics is solved numerically based on a new regularized inversion algorithm. In addition, the theory of sparsity promoting regularization is extended to situations in which sparsity cannot be expected and also to equations with non-injective operators.

La modélisation inverse de la dispersion atmosphérique consiste à reconstruire les caractéristiques d’une source (quantité de polluants rejetée, position) à partir de mesures de concentration dans l’air, en utilisant un modèle direct de dispersion et un algorithme d’inversion. Nous avons utilisé dans cette étude deux modèles directs de dispersion atmosphérique SIRANE (Soulhac, 2000; Soulhac et al., 2011) et SIRANERISK (Cierco et Soulhac, 2009a; Lamaison et al., 2011a, 2011b). Il s’agit de deux modèles opérationnels de « réseau des rues », basés sur le calcul du bilan de masse à différents niveaux du réseau. Leur concept permet de décrire correctement les différents phénomènes physiques de dispersion et de transport de la pollution atmosphérique dans des réseaux urbains complexes. L’étude de validation de ces deux modèles directs de dispersion a été effectuée après avoir évalué la fiabilité des paramétrages adoptés pour simuler les échanges verticaux entre la canopée et l'atmosphère, les transferts aux intersections de rues et la canalisation de l’écoulement à l’intérieur du réseau de rues. Pour cela, nous avons utilisé des mesures en soufflerie effectuées dans plusieurs configurations académiques. Nous avons développé au cours de cette thèse un système de modélisation inverse de dispersion atmosphérique (nommé ReWind) qui consiste à déterminer les caractéristiques d’une source de polluant (débit, position) à partir des concentrations mesurées, en résolvant numériquement le système matriciel linéaire qui relie le vecteur des débits au vecteur des concentrations. La fiabilité des résultats et l’optimisation des temps de calcul d’inversion sont assurées par le couplage de plusieurs méthodes mathématiques de résolution et d’optimisation, bien adaptées pour traiter le cas des problèmes mal posés. L’étude de sensibilité de cet algorithme d’inversion à certains paramètres d’entrée (comme les conditions météorologiques, les positions des récepteurs,…) a été effectuée en utilisant des observations synthétiques (fictives) fournies par le modèle direct de dispersion atmosphérique. La spécificité des travaux entrepris dans le cadre de ce travail a consisté à appliquer ReWind dans des configurations complexes de quartier urbain, et à utiliser toute la variabilité turbulente des mesures expérimentales obtenues en soufflerie pour qualifier ses performances à reconstruire les paramètres sources dans des conditions représentatives de situations de crise en milieu urbain ou industriel. L’application de l’approche inverse en utilisant des signaux instantanés de concentration mesurés en soufflerie plutôt que des valeurs moyennes, a montré que le modèle ReWind fournit des résultats d’inversion qui sont globalement satisfaisants et particulièrement encourageants en termes de reproduction de la quantité de masse totale de polluant rejetée dans l’atmosphère. Cependant, l’algorithme présente quelques difficultés pour estimer à la fois le débit et la position de la source dans certains cas. En effet, les résultats de l’inversion sont assez influencés par le critère de recherche (d’optimisation), le nombre de récepteurs impactés par le panache, la qualité des observations et la fiabilité du modèle direct de dispersion atmosphérique. / The aim of this study is to develop an inverse atmospheric dispersion model for crisis management in urban areas and industrial sites. The inverse modes allows for the reconstruction of the characteristics of a pollutant source (emission rate, position) from concentration measurements, by combining a direct dispersion model and an inversion algorithm, and assuming as known both site topography and meteorological conditions. The direct models used in these study, named SIRANE and SIRANERISK, are both operational "street network" models. These are based on the decomposition of the urban atmosphere into two sub-domains: the urban boundary layer and the urban canopy, represented as a series of interconnected boxes. Parametric laws govern the mass exchanges between the boxes under the assumption that the pollutant dispersion within the canopy can be fully simulated by modelling three main bulk transfer phenomena: channelling along street axes, transfers at street intersections and vertical exchange between a street canyon and the overlying atmosphere. The first part of this study is devoted to a detailed validation of these direct models in order to test the parameterisations implemented in them. This is achieved by comparing their outputs with wind tunnel experiments of the dispersion of steady and unsteady pollutant releases in idealised urban geometries. In the second part we use these models and experiments to test the performances of an inversion algorithm, named REWind. The specificity of this work is twofold. The first concerns the application of the inversion algorithm - using as input data instantaneous concentration signals registered at fixed receptors and not only time-averaged or ensemble averaged concentrations. - in urban like geometries, using an operational urban dispersion model as direct model. The application of the inverse approach by using instantaneous concentration signals rather than the averaged concentrations showed that the ReWind model generally provides reliable estimates of the total pollutant mass discharged at the source. However, the algorithm has some difficulties in estimating both emission rate and position of the source. We also show that the performances of the inversion algorithm are significantly influenced by the cost function used to the optimization, the number of receptors and the parameterizations adopted in the direct atmospheric dispersion model.

L’introduction de dégradations lors du processus de formation d’images est un phénomène inévitable: les images souffrent de flou et de la présence de bruit. Avec les progrès technologiques et les outils numériques, ces dégradations peuvent être compensées jusqu’à un certain point. Cependant, la qualité des images acquises est insuffisante pour de nombreuses applications. Cette thèse contribue au domaine de la restauration d’images. La thèse est divisée en cinq chapitres, chacun incluant une discussion détaillée sur différents aspects de la restauration d’images. La thèse commence par une présentation générale des systèmes d’imagerie et pointe les dégradations qui peuvent survenir ainsi que leurs origines. Dans certains cas, le flou peut être considéré stationnaire dans tout le champ de vue et est alors simplement modélisé par un produit de convolution. Néanmoins, dans de nombreux cas de figure, le flou est spatialement variable et sa modélisation est plus difficile, un compromis devant être réalisé entre la précision de modélisation et la complexité calculatoire. La première partie de la thèse présente une discussion détaillée sur la modélisation des flous spatialement variables et différentes approximations efficaces permettant de les simuler. Elle décrit ensuite un modèle de formation de l’image générique. Puis, la thèse montre que la restauration d’images peut s’interpréter comme un problème d’inférence bayésienne et ainsi être reformulé en un problème d’optimisation en grande dimension. La deuxième partie de la thèse considère alors la résolution de problèmes d’optimisation génériques, en grande dimension, tels que rencontrés dans de nombreux domaines applicatifs. Une nouvelle classe de méthodes d’optimisation est proposée pour la résolution des problèmes inverses en imagerie. Les algorithmes proposés sont aussi rapides que l’état de l’art (d’après plusieurs comparaisons expérimentales) tout en supprimant la difficulté du réglage de paramètres propres à l’algorithme d’optimisation, ce qui est particulièrement utile pour les utilisateurs. La troisième partie de la thèse traite du problème de la déconvolution aveugle (estimation conjointe d’un flou invariant et d’une image plus nette) et suggère différentes façons de contraindre ce problème d’estimation. Une méthode de déconvolution aveugle adaptée à la restauration d’images astronomiques est développée. Elle se base sur une décomposition de l’image en sources ponctuelles et sources étendues et alterne des étapes de restauration de l’image et d’estimation du flou. Les résultats obtenus en simulation suggèrent que la méthode peut être un bon point de départ pour le développement de traitements dédiés à l’astronomie. La dernière partie de la thèse étend les modèles de flous spatialement variables pour leur mise en oeuvre pratique. Une méthode d’estimation du flou est proposée dans une étape d’étalonnage. Elle est appliquée à un système expérimental, démontrant qu’il est possible d’imposer des contraintes de régularité et d’invariance lors de l’estimation du flou. L’inversion du flou estimé permet ensuite d’améliorer significativement la qualité des images. Les deux étapes d’estimation du flou et de restauration forment les deux briques indispensables pour mettre en oeuvre, à l’avenir, une méthode de restauration aveugle (c’est à dire, sans étalonnage préalable). La thèse se termine par une conclusion ouvrant des perspectives qui pourront être abordées lors de travaux futurs / Degradations of images during the acquisition process is inevitable; images suffer from blur and noise. With advances in technologies and computational tools, the degradations in the images can be avoided or corrected up to a significant level, however, the quality of acquired images is still not adequate for many applications. This calls for the development of more sophisticated digital image restoration tools. This thesis is a contribution to image restoration. The thesis is divided into five chapters, each including a detailed discussion on different aspects of image restoration. It starts with a generic overview of imaging systems, and points out the possible degradations occurring in images with their fundamental causes. In some cases the blur can be considered stationary throughout the field-of-view, and then it can be simply modeled as convolution. However, in many practical cases, the blur varies throughout the field-of-view, and thus modeling the blur is not simple considering the accuracy and the computational effort. The first part of this thesis presents a detailed discussion on modeling of shift-variant blur and its fast approximations, and then it describes a generic image formation model. Subsequently, the thesis shows how an image restoration problem, can be seen as a Bayesian inference problem, and then how it turns into a large-scale numerical optimization problem. Thus, the second part of the thesis considers a generic optimization problem that is applicable to many domains, and then proposes a class of new optimization algorithms for solving inverse problems in imaging. The proposed algorithms are as fast as the state-of-the-art algorithms (verified by several numerical experiments), but without any hassle of parameter tuning, which is a great relief for users. The third part of the thesis presents an in depth discussion on the shift-invariant blind image deblurring problem suggesting different ways to reduce the ill-posedness of the problem, and then proposes a blind image deblurring method using an image decomposition for restoration of astronomical images. The proposed method is based on an alternating estimation approach. The restoration results on synthetic astronomical scenes are promising, suggesting that the proposed method is a good candidate for astronomical applications after certain modifications and improvements. The last part of the thesis extends the ideas of the shift-variant blur model presented in the first part. This part gives a detailed description of a flexible approximation of shift-variant blur with its implementational aspects and computational cost. This part presents a shift-variant image deblurring method with some illustrations on synthetically blurred images, and then it shows how the characteristics of shift-variant blur due to optical aberrations can be exploited for PSF estimation methods. This part describes a PSF calibration method for a simple experimental camera suffering from optical aberration, and then shows results on shift-variant image deblurring of the images captured by the same experimental camera. The results are promising, and suggest that the two steps can be used to achieve shift-variant blind image deblurring, the long-term goal of this thesis. The thesis ends with the conclusions and suggestions for future works in continuation of the current work

Cette thèse s’inscrit dans le cadre de la conception, l’analyse et la mise en œuvre d’algorithmes efficaces et fiables pour la résolution de problèmes d’optimisation non linéaire avec contraintes. Nous présentons trois nouveaux algorithmes fortement primaux-duaux pour résoudre ces problèmes. La première caractéristique de ces algorithmes est que le contrôle des itérés s’effectue dans l’espace primal-dual tout au long du processus de la minimisation, d’où l’appellation “fortement primaux-duaux”. En particulier, la globalisation est effectuée par une méthode de recherche linéaire qui utilise une fonction de mérite primale-duale. La deuxième caractéristique est l’introduction d’une régularisation naturelle du système linéaire qui est résolu à chaque itération pour calculer une direction de descente. Ceci permet à nos algorithmes de bien se comporter pour résoudre les problèmes dégénérés pour lesquels la jacobienne des contraintes n’est pas de plein rang. La troisième caractéristique est que le paramètre de pénalisation est autorisé à augmenter au cours des itérations internes, alors qu’il est généralement maintenu constant. Cela permet de réduire le nombre d’itérations internes. Une étude théorique détaillée incluant l’analyse de convergence globale des itérations internes et externes, ainsi qu’une analyse asymptotique a été présentée pour chaque algorithme. En particulier, nous montrons qu’ils jouissent d’un taux de convergence rapide, superlinéaire ou quadratique. Ces algorithmes sont implémentés dans un nouveau solveur d’optimisation non linéaire qui est appelé SPDOPT. Les bonnes performances de ce solveur ont été montrées en effectuant des comparaisons avec les codes de références IPOPT, ALGENCAN et LANCELOT sur une large collection de problèmes. / This thesis focuses on the design, analysis, and implementation of efficient and reliable algorithms for solving nonlinearly constrained optimization problems. We present three new strongly primal-dual algorithms to solve such problems. The first feature of these algorithms is that the control of the iterates is done in both primal and dual spaces during the whole minimization process, hence the name “strongly primal-dual”. In particular, the globalization is performed by applying a backtracking line search algorithm based on a primal-dual merit function. The second feature is the introduction of a natural regularization of the linear system solved at each iteration to compute a descent direction. This allows our algorithms to perform well when solving degenerate problems for which the Jacobian of constraints is rank deficient. The third feature is that the penalty parameter is allowed to increase along the inner iterations, while it is usually kept constant. This allows to reduce the number of inner iterations. A detailed theoretical study including the global convergence analysis of both inner and outer iterations, as well as an asymptotic convergence analysis is presented for each algorithm. In particular, we prove that these methods have a high rate of convergence : superlinear or quadratic. These algorithms have been implemented in a new solver for nonlinear optimization which is called SPDOPT. The good practical performances of this solver have been demonstrated by comparing it to the reference codes IPOPT, ALGENCAN and LANCELOT on a large collection of test problems.

Le but de cette thèse est d'étudier lagravité quantique bidimensionnelle. Nousnous intéressons plus particulièrement auxapproches dans le continu. Ces dernièresreposent principalement sur l'action deLiouville qui décrit le couplage entre théorieconforme et gravité. Si cette action, bienconnue, est très bien comprise, la mesure del'intégrale fonctionnelle sur l'espace desmétriques pose plus de problèmes. Toutefois,sous l'hypothèse simplificatrice d'une mesurede champ libre, la dépendance en l'aire de lafonction de partition de la gravité quantiqueen présence de matière conforme a pu êtreétablie. Malgré l'hypothèse assez forte sur lamesure d'intégration, cette formule (diteKPZ), a été confirmée par des calculs issusde méthodes discrètes, et ce dans plusieurscas particuliers. Grâce à une nouvelle méthode derégularisation spectrale en espace courbe,cette mesure d'intégration a récemment puêtre proprement définie. Dans cette thèse,un calcul perturbatif de la fonction departition à aire fixée est mené, jusqu'à troisboucles, en considérant l'action de Liouvilleet des surfaces de Kähler de genrequelconque (qui coïncident avec l'ensembledes surfaces à deux dimensions). Desdivergences apparaissant dans les calculs, ilest nécessaire de renormaliser les actions.Cette renormalisation peut être interprétéecomme une renormalisation de la mesured'intégration. Nos résultats à deux bouclessont finis, indépendants de la régularisationet compatibles avec le résultat KPZ, maisdépendent d'un paramètre libre. L'étude àtrois boucles suggère que la théorie resterenormalisable aux ordres supérieurs maisdépend de nouveaux paramètres à chaqueordre. Ces résultats ont été généralisé dansle cas du tore au couplage à de la matièrenon-conforme. / Nowadays, two-dimensional quantumgravity can be studied in two differentapproaches, one involving discrete theories(triangulation, matrix model...), the othercontinuous ones, mainly based on the socalled Liouville action which universallydescribes the coupling of any conformal fieldtheory to gravity. While the Liouville action isrelatively well understood, the appropriatefunctional integral measure is however rathercomplicated. Nevertheless, a formula for thearea dependence of the quantum gravitypartition function in the presence of conformalmatter has been obtained, under thesimplifying assumption of a free-fieldmeasure. Notwithstanding its non-rigorousderivation, this formula, often referred to asthe KPZ formula, has since been verified inmany instances and has scored manysuccesses. Recent developments of efficient multiloopregularization methods on curved spacetimesopened the way for a precise and welldefinedperturbative computation of the fixedareapartition function in the Kählerformalism. In this work, a first-principlescomputation of the fixed-area partitionfunction in the Liouville theory is performed,up to three loops. Among other things, therole of the non-trivial quantum gravityintegration measure is highlighted.Renormalization is required and may beinterpreted as a renormalization of theintegration measure. This leads to a finite andregularization-independent result at two loops,that is more general than the KPZ result,although compatible. Finiteness andregularization-independence seem alsopossible at three loops. These results aregeneralized to the coupling to non-conformalmatter on the torus.

La dualité et la robustesse sont des outils essentiels dans les processus d'aide à la décision. Cette thèse concerne trois thèmes: dualité en optimisation convexe conique à données incertaines, dualité et régularisation en convexité généralisée, et la maximisation du rayon de robustesse en optimisation continue. Dans la première partie de ce travail, on considère les notions de pire valeur et de valeur robuste d'un problème d'optimisation conique à données incertaines. On donne une condition nécessaire et suffisante pour l'égalité entre la pire valeur et la valeur robuste de ce problème avec exactitude de la pire valeur. On déduit une condition suffisante permettant d'obtenir la propriété de dualité robuste forte pour ce problème. La deuxième partie est consacrée à la dualité et à la régularisation de fonctions numériques à valeurs réelles étendues. Deux points de vue sont considérés: l'approche par les niveaux et l'approche par les épigraphes. On étend ainsi à la convexité généralisée des résultats récents concernant le passage de la dualité quasi-convexe à la dualité convexe. On applique cette théorie à un problème d'optimisation pour déduire un résultat de dualité forte. La troisième partie de ce travail porte une étude du problème de maximisation du rayon de stabilité. On définit le rayon de robustesse pour un problème de décision en milieu incertain, et on étudie certaines de ces propriétés analytiques (concavité et semi-continuité). La contrepartie robuste d'un problème d'optimisation à données incertaines au sens du rayon de robustesse est introduite. On étudie le lien en termes d'ensemble de solutions optimales entre la contrepartie robuste au sens du rayon de robustesse et celle au sens de l'optimisation robuste d'un problème incertain d'optimisation continue. Un modèle générique du problème de maximisation du rayon de robustesse regroupant une large classe de cas pratique est proposé. On examine ce modèle dans un cas polyédral, dans le cas de la régression linéaire puis dans un cas quadratique. Notre stratégie dans ces différents cas, consiste à expliciter le rayon de robustesse et/ou à transformer le problème de maximisation du rayon de stabilité en un programme tractable. Une application à un problème de conception d'antenne circulaire est proposée dans le cas de la régression et une application au calcul d'un estimateur robuste est proposée dans le cas quadratique. / Duality and robustness are two important tools in decision making process. This thesis deals with tree topics : duality for an uncertain convex conical optimization problem, duality and regularity in generalized convexity, and the maximization of the stability radius. In the first part of this work, we consider the notions of worst value and robust value of an uncertain convex conical optimization problem. We give a necessary and sufficient condition to obtain the equality between the robust value and the worst value with exactness for the worst value. We derive a sufficient condition to obtain a robust strong duality property for this problem. The second part of this work is devoted to duality and regularity of the extended real-valued functions. Two points of view are considered: the sub-level set approach and the epigraphical approach. We then extend some recent results concerning the passage from the quasi-convex duality to convex duality to the generalized convexity. We apply this theory to an optimization problem to derive a strong duality property for this problem. The third part of this work is devoted to the study of the problem of maximization of the stability radius. We define the stability radius for a decision problem under data uncertainty, and study some of its analytical properties (e.g concavity and upper semi-continuity). The robust counterpart of an uncertain optimization problem according to the stability radius is introduced. We study the relation between the solution set of this counterpart and the solution set of the robust counterpart according to the robust optimization approach. We propose a generic model of the maximization of stability radius which covers a large class of applications. We study this problem in a polyhedral case, in the case of regression and in quadratic case. In each case, we compute the stability radius and/ or transform the problem of maximization of the stability radius to a tractable problem. An application to a circular antenna design problem is given in the regression case, and an application to compute a robust estimator is provided in the quadratic case.