Cette thèse est consacrée, d'une part, à l'étude d'existence de solutions pour des problèmes d'évolution et, d'autre part, à la stabilité de la propriété de prox-régularité ensembliste. Nous étudions dans la première partie des processus de rafle de Moreau perturbés et discontinu du premier et du second ordre. L'ensemble mouvant est prox-régulier dans un espace de Hilbert réel quelconque et sa variation est contrôlé par une mesure de Radon. Des applications à la théorie de la complémentarité et à celle des inéquations variationnelles sont présentées. Dans la seconde partie, on donne des conditions suffisantes assurant la prox-régularité d'ensembles décrit par des contraintes non nécessairement lisses sous forme d'inégalités et/ ou d'égalités et plus généralement d'ensembles de solutions d'équations généralisées. On y développe également des conditions vérifiables assurant la préservation de la prox-régularité vis-à-vis d'opérations ensemblistes : les cas de l'intersection, d'image directe, de pré-image, d'union et projection sur un sous-espace sont considérés. / In this dissertation, we study, on the one hand, the existence of solutions for some evolution problems and, on the other hand, the stability of prox-regularity under set operations. The first topic is devoted to first and second order nonconvex perturberd Moreau's sweeping processes in infinite dimensional framework. The moving set is assumed to be prox-regular and moved in a bounded variation way. Applications to the theory of complementarity problems and evolution variational inequalities are given. In the other topic, we first give verifiable sufficient conditions ensuring the prox-regularity of constrained sets and more generally for solution sets of generalized equations. We also develop the preservation of prox-regularity under set operations as intersection, direct image, inverse image, union and projection along a vector space.

Ce travail est divisé en deux parties: Dans la première partie, on présente un résultat d'intégration dans les espaces localement convexes valable pour une longe classe des fonctions non-convexes. Cela nous permet de récupérer l'enveloppe convexe fermée d'une fonction à partir du sous-différentiel convexe de cette fonction. Motivé par ce résultat, on introduit la classe des espaces ``Subdifferential Dense Primal Determined'' (SDPD). Ces espaces jouissent des conditions nécessaires permettant d'appliquer le résultat ci-dessus. On donne aussi une interprétation géométrique de ces espaces, appelée la Propriété Radon-Nikod'ym de Faces (FRNP). Dans la seconde partie, on étudie dans le contexte d'espaces d'Hilbert, la relation entre la lissité de la frontière d'un ensemble prox-régulier et la lissité de sa projection métrique. On montre que si un corps fermé possède une frontière $mathcal{C}^{p+1}$-lisse (avec $pgeq 1$), alors sa projection métrique est de classe $mathcal{C}^p$ dans le tube ouvert associé à sa fonction de prox-régularité. On établit également une version locale du même résultat reliant la lissité de la frontière autour d'un point à la prox-régularité en ce point. On étudie par ailleurs le cas où l'ensemble est lui-même une $mathcal{C}^{p+1}$-sous-variété. Finalement, on donne des réciproques de ces résultats. / This work is divided in two parts: In the first part, we present an integration result in locally convex spaces for a large class of nonconvex functions which enables us to recover the closed convex envelope of a function from its convex subdifferential. Motivated by this, we introduce the class of Subdifferential Dense Primal Determined (SDPD) spaces, which are those having the necessary condition which allows to use the above integration scheme, and we study several properties of it in the context of Banach spaces. We provide a geometric interpretation of it, called the Faces Radon-Nikod'ym property. In the second part, we study, in the context of Hilbert spaces, the relation between the smoothness of the boundary of a prox-regular set and the smoothness of its metric projection. We show that whenever a set is a closed body with a $mathcal{C}^{p+1}$-smooth boundary (with $pgeq 1$), then its metric projection is of class $mathcal{C}^{p}$ in the open tube associated to its prox-regular function. A local version of the same result is established as well, namely, when the smoothness of the boundary and the prox-regularity of the set are assumed only near a fixed point. We also study the case when the set is itself a $mathcal{C}^{p+1}$-submanifold. Finally, we provide converses for these results.

This dissertation aims to develop efficient algorithms with improved scalability and stability properties for large-scale optimization and optimization under uncertainty, and to bridge some of the gaps between modern optimization theories and recent applications emerging in the Big Data environment. To this end, the dissertation is dedicated to two important subjects -- i) Large-scale Convex Composite Optimization and ii) Error-in-Measurement Optimization. In spite of the different natures of these two topics, the common denominator, to be presented, lies in their accommodation for systematic use of saddle point techniques for mathematical modeling and numerical processing. The main body can be split into three parts. In the first part, we consider a broad class of variational inequalities with composite structures, allowing to cover the saddle point/variational analogies of the classical convex composite minimization (i.e. summation of a smooth convex function and a simple nonsmooth convex function). We develop novel composite versions of the state-of-the-art Mirror Descent and Mirror Prox algorithms aimed at solving such type of problems. We demonstrate that the algorithms inherit the favorable efficiency estimate of their prototypes when solving structured variational inequalities. Moreover, we develop several variants of the composite Mirror Prox algorithm along with their corresponding complexity bounds, allowing the algorithm to handle the case of imprecise prox mapping as well as the case when the operator is represented by an unbiased stochastic oracle. In the second part, we investigate four general types of large-scale convex composite optimization problems, including (a) multi-term composite minimization, (b) linearly constrained composite minimization, (c) norm-regularized nonsmooth minimization, and (d) maximum likelihood Poisson imaging. We demonstrate that the composite Mirror Prox, when integrated with saddle point techniques and other algorithmic tools, can solve all these optimization problems with the best known so far rates of convergences. Our main related contributions are as follows. Firstly, regards to problems of type (a), we develop an optimal algorithm by integrating the composite Mirror Prox with a saddle point reformulation based on exact penalty. Secondly, regards to problems of type (b), we develop a novel algorithm reducing the problem to solving a ``small series'' of saddle point subproblems and achieving an optimal, up to log factors, complexity bound. Thirdly, regards to problems of type (c), we develop a Semi-Proximal Mirror-Prox algorithm by leveraging the saddle point representation and linear minimization over problems' domain and attain optimality both in the numbers of calls to the first order oracle representing the objective and calls to the linear minimization oracle representing problem's domain. Lastly, regards to problem (d), we show that the composite Mirror Prox when applied to the saddle point reformulation circumvents the difficulty with non-Lipschitz continuity of the objective and exhibits better convergence rate than the typical rate for nonsmooth optimization. We conduct extensive numerical experiments and illustrate the practical potential of our algorithms in a wide spectrum of applications in machine learning and image processing. In the third part, we examine error-in-measurement optimization, referring to decision-making problems with data subject to measurement errors; such problems arise naturally in a number of important applications, such as privacy learning, signal processing, and portfolio selection. Due to the postulated observation scheme and specific structure of the problem, straightforward application of standard stochastic optimization techniques such as Stochastic Approximation (SA) and Sample Average Approximation (SAA) are out of question. Our goal is to develop computationally efficient and, hopefully, not too conservative data-driven techniques applicable to a broad scope of problems and allowing for theoretical performance guarantees. We present two such approaches -- one depending on a fully algorithmic calculus of saddle point representations of convex-concave functions and the other depending on a general approximation scheme of convex stochastic programming. Both approaches allow us to convert the problem of interests to a form amenable for SA or SAA. The latter developments are primarily focused on two important applications -- affine signal processing and indirect support vector machines.

The main objective of this Thesis is the synthesis, characterization and application in the PROX reaction of several series of catalysts synthesized using different methods, in order to find efficient materials with high catalytic activity. This work has been divided in six chapters. Chapter I presents an introduction about current energy problems and hydrogen (energy carrier) as a solution, with its limitations and advances on its use: storage, transport and security. Finally, its use as a fuel in PEMFC (Proton Exchange Membrane Fuel Cells) and the advantages comparing other existent fuel cells has been discussed. A brief summary was done about the catalytic systems studied in literature for PROX reaction and their characteristics. Following, Chapter 2 describes all the characterization techniques which were used to study the properties of the synthesized supports and catalysts, together with the experimental system employed for the catalytic tests. Most of these equipments belong to SSTTI of University of Alicante or are hand-made systems in the LMA group. DRIFTs and DTP were done at TUDelft, Catalysis Engineering Section. Next chapters contain the most important results obtained during the complete research work; they have been divided in two parts. On one hand, Chapter 3 describes the synthesis of pure TiO2 using five different methods, and its use as platinum support for PROX catalysts. On the other hand, taking into account the obtained results, three synthesis methods were chosen, and the study was centered in the addition of CeO2 to TiO2. Chapter 4 discusses the TixCe(1-x)O2 series synthesized using the sol-gel method. In Chapter 5 a solvothermal procedure was employed for the synthesis of supports with similar composition and, finally, impregnation of cerium over commercial P25 titania was compared in Chapter 6. Each chapter contains a complete study of characterization of both supports and catalysts. Synthesis parameters, pretreatment and reaction conditions were also modified for the best catalyst of the three series. Analyzing the catalysts’ behavior, a reaction mechanism was proposed. Finally, general conclusions summarize the most relevant results obtained in each chapter.

<p>Nano-structures were investigated for the advancement of energy conversion technology because of their enhanced catalytic, thermal, and physiochemical interfacial properties and increased solar absorption. Hydrogen is a widely investigated and proven fuel and energy carrier for promising "green" technologies such as fuel cells. Difficulties involving storage, transport, and availability remain challenges that inhibit the widespread use of hydrogen fuel. For these reasons, in-situ hydrogen production has been at the forefront of research in the renewable and sustainable energy field. A common approach for hydrogen generation is the reforming of alcoholic and hydrocarbon fuels from fossil and renewable sources to a hydrogen-rich gas mixture.</p><p>Unfortunately, an intrinsic byproduct of any fuel reforming reaction is toxic and highly reactive CO, which has to be removed before the hydrogen gas can be used in fuel cells or delicate chemical processes. In this work, Au/alpha-Fe2O3 catalyst was synthesized using a modified co-precipitation method to generate an inverse catalyst model. The effects of introducing CO2 and H2O during preferential oxidation (PROX) of CO were investigated. For realistic conditions of (bio-)fuel reforming, 24% CO2 and 10% water the highest document conversion, 99.85% was achieved. The mechanism for PROX is not known definitively, however, current literature believes the gold particle size is the key. In contrast, we emphasize the tremendous role of the support particle size. A particle size study was performed to have in depth analysis of the catalysts morphology during synthesis. With this study we were also able to modify how the catalyst was made to further reduce the particle size of the support material leading to ~99.9% conversion. We also showed that the resulting PROX output gas could power a PEM fuel cell with only a 4% drop in power without poisoning the membrane electrode assembly.</p><p> The second major aim of this study is to develop an energy-efficient technology that fuses photothermal catalysis and plasmonic phenomena. Although current literature has claimed that the coupling of these technologies is impossible, here we demonstrate the fabrication of reaction cells for plasmon-induced photo-catalytic hydrogen production. The localized nature of the plasmon resonance allows the entire system to remain at ambient temperatures while a high-temperature methanol reformation reaction occurs at the plasmonic sites. Employing a nanostructured plasmonic substrate, we have successfully achieved sufficient thermal excitement (via localized surface plasmon resonance (LSPR)) to facilitate a heterogeneous chemical reaction. The experimental tests demonstrate that hydrogen gas can indeed be generated in a cold reactor, which has never been done before. Additionally, the proposed method has the highest solar absorption out of several variations and significantly reduces the cost, while increasing the efficiency of solar fuels.</p> / Dissertation

In this study, the effect of Pt particle size on the reaction rate and selectivity of preferential oxidation of CO (PROX) reaction was investigated on Pt/Al2O3. 2% Pt/&amp / #947 / -Al2O3 catalysts were prepared by incipient wetness method / the particle size of the catalysts was modified by calcination temperature and duration. Therefore, the relative amounts of low and high coordination atoms on the metal particle surface can be changed. Over these catalysts, first, the CO oxidation reaction was studied in the absence of hydrogen. The catalyst having the highest dispersion, i.e., lowest metal particle sizes, had the highest activity as indicated by its lowest light-off temperature. On the other hand, the turnover frequencies (TOF) of the catalysts were increasing with decreasing dispersion. The activation energy of the catalysts were also compared and examined: as the particle size increased, the activation energy decreased. In the second part, preferential oxidation of CO reaction in the presence of hydrogen was studied. Both CO conversion and selectivity first increased with increasing reaction temperature, then exhibited a maximum, and finally decreased. Both CO conversion and selectivity did not show any trend for different dispersed catalysts for &amp / #955 / (2PO2/PCO) was 1. In order to reach a definite conclusion about the structure sensitivity of selective CO oxidation, the experiments with different &amp / #955 / &rsquo / s and space times over the same catalysts should be performed.

139 f. / Submitted by Ana Hilda Fonseca (anahilda@ufba.br) on 2013-03-22T17:52:48Z No. of bitstreams: 1 Efeito do lantânio nas propriedades de catalisadores de cobre, cério e zircônio, na reação de PROX.pdf: 1865766 bytes, checksum: fc63e93a913ab80e690a741cf6ea78bd (MD5) / Approved for entry into archive by Ana Hilda Fonseca(anahilda@ufba.br) on 2013-06-05T17:31:16Z (GMT) No. of bitstreams: 1 Efeito do lantânio nas propriedades de catalisadores de cobre, cério e zircônio, na reação de PROX.pdf: 1865766 bytes, checksum: fc63e93a913ab80e690a741cf6ea78bd (MD5) / Made available in DSpace on 2013-06-05T17:31:16Z (GMT). No. of bitstreams: 1 Efeito do lantânio nas propriedades de catalisadores de cobre, cério e zircônio, na reação de PROX.pdf: 1865766 bytes, checksum: fc63e93a913ab80e690a741cf6ea78bd (MD5) Previous issue date: 2012 / CAPES / Devido ao desenvolvimento das células a combustível de membrana trocadora de prótons (PEMFCs), abastecidas com hidrogênio, é necessário encontrar processos para a purificação desse gás. Os processos tradicionais de produção, como a reforma a vapor do gás natural, produzem misturas ricas em hidrogênio com quantidades baixas de monóxido de carbono (≈ 0,5-2,0%) que, no entanto, são suficientes para envenenar os eletrodos de platina das PEMFCs. A oxidação preferencial do monóxido de carbono em misturas ricas em hidrogênio (PROX) tem sido apontada como uma das rotas mais adequadas para a purificação de hidrogênio para células a combustível. Vários estudos têm mostrado que os catalisadores baseados em óxidos de cobre e cério ou óxidos de cobre, cério e zircônio, são altamente ativos e seletivos para a produção de dióxido de carbono na oxidação preferencial do monóxido de carbono. Outros estudos têm mostrado que a dopagem do óxido de cério ou do óxido de cério e zircônio com íons terras-raras, tal como o íon La3+, produz sólidos com área superficial específica e capacidade de estocagem de oxigênio mais elevadas. Com o objetivo de encontrar catalisadores mais eficientes para a reação de PROX, neste trabalho estudou-se o efeito do lantânio sobre as propriedades de catalisadores baseados em cobre, cério e zircônio, concentrando-se no aumento da área superficial específica e da capacidade de estocagem de oxigênio. Foram preparados catalisadores baseados em cobre, cério e lantânio (CuO-Ce1-xLaxO2-x/2), bem como cobre, cério, zircônio e lantânio (CuO-Ce0,5-x/2Zr0,5-x/2LaxO2-x/2), com composições diferentes (x = 0,0; 0,05; 0,10; 0,15; 0,20), 6 % em massa de Cu, além de catalisadores isentos de cério (CuO-ZrO2 e CuO-La2O3), para comparação, através de precipitação simultânea utilizando hidróxido de potássio como agente precipitante. As amostras foram caracterizadas por análise química elementar, termogravimetria, espectroscopia no infravermelho com transformada de Fourier, difração de raios X, medidas de área superficial específica, redução à temperatura programada, medidas de capacidade de estocagem de oxigênio e troca isotópica com oxigênio-18 (18O2). Os catalisadores foram avaliados na oxidação preferencial do monóxido de carbono na faixa de 150 a 300 °C. Observou-se que a adição de lantânio aumenta a área superficial específica dos catalisadores, devido à diminuição do tamanho médio de cristal, no caso dos catalisadores isentos de zircônio e, provavelmente, devido a um aumento da porosidade, no caso dos catalisadores contendo zircônio. Além disso, verificou-se que pequenas quantidades de lantânio aumentam a capacidade de estocagem de oxigênio dos sólidos e aumentam a mobilidade do oxigênio. No entanto, a adição de lantânio não melhora o desempenho dos catalisadores na oxidação preferencial do monóxido de carbono, um fato que foi relacionado com a diminuição do teor de cério nos catalisadores à medida que o teor de lantânio é aumentado. Isto pode ser relacionado com a interface entre as partículas de óxido de cobre e óxido de cério, onde ocorre a reação, que diminui à medida que aumenta a quantidade de lantânio nos catalisadores. Além disso, a adição de 10 % de dióxido de carbono, durante a reação a 150 °C, diminui a atividade dos catalisadores, o que foi atribuído à quimissorção do dióxido de carbono no óxido de cério. Por outro lado, a adição de 2 % de água não altera significativamente a atividade ou a seletividade dos catalisadores testados. O catalisador baseado em cobre, cério e zircônio, isento de lantânio, foi o mais ativo e seletivo. / Salvador

Submitted by Ana Hilda Fonseca (anahilda@ufba.br) on 2016-05-02T19:10:29Z No. of bitstreams: 1 Dissertação_Luiz Henrique_versão final.pdf: 2601378 bytes, checksum: c42dd329851055be9a8ef4218dced85c (MD5) / Approved for entry into archive by Ana Hilda Fonseca (anahilda@ufba.br) on 2016-05-12T17:46:39Z (GMT) No. of bitstreams: 1 Dissertação_Luiz Henrique_versão final.pdf: 2601378 bytes, checksum: c42dd329851055be9a8ef4218dced85c (MD5) / Made available in DSpace on 2016-05-12T17:46:40Z (GMT). No. of bitstreams: 1 Dissertação_Luiz Henrique_versão final.pdf: 2601378 bytes, checksum: c42dd329851055be9a8ef4218dced85c (MD5) / CNPq / Nos últimos anos, as células a combustível têm atraído cada vez mais atenção, em todo o mundo, por causa da sua habilidade de produzir energia de forma lima e eficiente. Quando alimentados com hidrogênio, esses dispositivos produzem apenas água e não emitem nenhum poluente. Entre os diversos tipos de células a combustível, as células a combustível de membrana de troca protônica (PEMFC) são as mais adequadas para aplicações móveis. Entretanto, o hidrogênio é obtido principalmente através da reforma a vapor do gás natural e, então, contém quantidades baixas de monóxido de carbono (0,5-2,0%), que são suficientes para envenenar os eletrodos de platina das células do tipo PEMFC. Visando a obter catalisadores mais eficientes para essa reação, neste trabalho, foi estudado o efeito do samário nas propriedades de catalisadores baseados em óxidos de cobre e de cério. Os catalisadores baseados em cobre, cério e samário (CuO-Ce1-xSmxO2-x/2), com composições diferentes (x = 0,0; 0,10; 0,20 e 0,50), 25 % em mol de Cu, foram preparados através de precipitação simultânea, utilizando hidróxido de sódio como agente precipitante. As amostras foram caracterizadas por análise química elementar, espectroscopia no infravermelho com transformada de Fourier, difração de raios X, medidas de área superficial específica e de porosidade, espectroscopia Raman e redução à temperatura programada. Os catalisadores foram avaliados na oxidação preferencial do monóxido de carbono na faixa de temperatura entre 50 e 250 °C. Observou-se que o samário foi incorporado na rede da céria e que a sua adição não causou variação na área superficial específica dos catalisadores, exceto na amostra contendo o teor mais alto de samário. Além disso, o samário não melhorou a atividade catalítica, um fato que foi associado com a diminuição do teor de cério nos catalisadores, diminuindo a interface entre as partículas de óxido de cobre e óxido de cério, onde ocorre a reação. A adição de dióxido de carbono (10 % mol) ao meio reacional causou uma diminuição da conversão do monóxido de carbono, provavelmente devido ao bloqueio dos sítios; entretanto, a seletividade, não variou. O catalisador mais promissor foi aquele com 20% mol de samário, que mostrou a seletividade a dióxido de carbono mais elevada / In last years, fuel cells have attracted increasing attention worldwide because of their ability in producing efficient and clean energy. When fed with hydrogen, these devices produce only water and emit no pollutant. Among the several kinds of fuel cells, the proton exchange membrane fuel cells (PEMFC) are especially suitable for mobile applications. However, hydrogen is mainly obtained by steam reforming of natural gas and then contains low amounts of carbon monoxide (0.5-2.0%), which are enough to poison the platinum electrodes of the proton exchange membrane fuel cells (PEMFC). In order to overcome this drawback, the preferential oxidation of carbon monoxide (CO-PROX) in the presence of an excess of hydrogen is an effective way for removing carbon monoxide up to amounts lower than 1 ppm. Aiming to find efficient catalysts for this reaction, the effect of samarium on the properties of catalysts based on copper oxides and cerium was studied in this work. Catalysts based on copper, cerium and samarium (CuO-Ce1-xSmxO2-x/2) with different compositions (x = 0.0, 0.10, 0.20 and 0.50) and 25 mol% Cu were prepared, by simultaneous precipitation using sodium hydroxide as the precipitant. The samples were characterized by elemental chemical analysis, Fourier transform infrared spectroscopy, X-ray diffraction, specific surface area and porosity measurements, Raman spectroscopy and temperature programmed reduction. The catalysts were evaluated in the preferential oxidation of carbon monoxide in the temperature range of 50 to 250 °C. It was observed that samarium was incorporated into ceria lattice and that its addition caused no change in the specific surface area, except for the samarium-richest sample. In addition, samarium did not improve the catalytic activity, a fact that was associated with the decrease of cerium content, decreasing the interface between copper oxide and cerium oxide, where the reaction occurs. The selectivity to carbon dioxide changed due to samarium depending on its amount. The addition of carbon dioxide (10% mole) to the reaction medium caused a decrease in carbon monoxide conversion, probably due to the sites blockage; however, the selectivity did not change. The most promising catalyst was that with 20% mole of samarium, which showed the highest selectivity to carbon dioxide.

Esta tesis consiste en la implementación de la tecnología de impresión 30 como una herramienta para el diseño y fabricación de soportes monolíticos que mejoran las prestaciones de los soportes convencionales. En un primer enfoque se ha empleado la estereolitografía (impresión 30) para la preparación directa de estructuras monolíticas de resina polimérica. Estos monolitos poliméricos con diferentes diseños geométricos se han empleado como soporte de la fase activa Cu0/Ce02 y su rendimiento fue estudiado en la reacción de oxidación preferencial de C0 (C0-Prüx). Un segundo enfoque ha consistido en la preparación de plantillas (moldes) mediante la tecnología de impresión 30 de modelado por deposición fundida, las cuales junto con un procedimiento de síntesis de hidrogeles de resorcinol y formaldehído han permitido obtener estructuras monolíticas de carbón con diferentes configuraciones geométricas de sus canales y una porosidad definida por las condiciones de síntesis. Estos monolitos de carbón se han empleado con éxito como soportes de las fases activas Cu0/Ce02 y Ni/Ce02, y su rendimiento catalítico fue estudiado en la reacción C0-Prüx y la reacción de metanación de C02, respectivamente.

The Preferential CO Oxidation (CO-PROX) is a promising catalytic strategy to remove CO residual content from H2-rich streams. Mixed copper and cerium oxide catalysts are materials that display an excellent performance towards COPROX reaction by means of synergistic interaction the copper and cerium-rich phases. Alternatively, mixed manganese oxides are proposed as active supports with very positive catalytic features when these are loaded with copper species. This Project Thesis comprises a detailed study on the implementation of copper oxide – manganese oxide catalysts in CO-PROX reaction and the establishment of a critical comparison with regards to the consolidated cerium-based catalysts.