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.

Increasing demands regarding performance, safety and environmental compatibility of hydraulic mobile machines in combination with rising cost pressures create a growing need for specialized optimization of hydraulic systems; particularly with regard to hydraulic reservoirs. In addition to the secondary function of cooling the oil, two main functions of the hydraulic reservoir are oil storage and de-aeration of the hydraulic oil. While designing hydraulic reservoirs regarding oil storage is quite simple, the design regarding de-aeration can be quite difficult. The author presents an approach to a system optimization of hydraulic reservoirs which combines experimental and numerical techniques to resolve some challenges facing hydraulic tank design. Specialized numerical tools are used in order to characterize the de-aeration performance of hydraulic tanks. Further the simulation of heat transfer is used to study the cooling function of hydraulic tank systems with particular attention to plastic tank solutions. To accompany the numerical tools, experimental test rigs have been built up to validate the simulation results and to provide additional insight into the design and optimization of hydraulic tanks which will be presented as well.

Computational methods in single molecule localization microscopy Abstract Fluorescence microscopy is one of the chief tools used in biomedical research as it is a non invasive, non destructive, and highly specific imaging method. Unfortunately, an optical microscope is a diffraction limited system. Maximum achievable spatial resolution is approximately 250 nm laterally and 500 nm axially. Since most of the structures in cells researchers are interested in are smaller than that, increasing resolution is of prime importance. In recent years, several methods for imaging beyond the diffraction barrier have been developed. One of them is single molecule localization microscopy, a powerful method reported to resolve details as small as 5 nm. This approach to fluorescence microscopy is very computationally intensive. Developing methods to analyze single molecule data and to obtain super-resolution images are the topics of this thesis. In localization microscopy, a super-resolution image is reconstructed from a long sequence of conventional images of sparsely distributed single photoswitchable molecules that need to be sys- tematically localized with sub-diffraction precision. We designed, implemented, and experimentally verified a set of methods for automated processing, analysis and visualization of data acquired...

M.Tech. (Department of Chemical Engineering, Faculty of Engineering and Technology), Vaal University of Technology. / The generation of waste tires is one of the most serious environmental problems in the modern world due to the increased use of auto mobiles all over the world. Currently there is a problem with the disposal of waste tires generated since there are strict regulations concerning their disposal through landfill sites. Therefore, there is a need to find ways of disposing these waste tires which pose serious health and environmental problem. The pyrolysis of the waste tires has been recognised as the most promising method to dispose the waste tires because it can reduce the weight of the waste tires to 10% of its original weight and produce products such as pyrolysis oil, pyrolysis char, and pyrolysis char. These products can be further processed to produce value added products. The char produced from the pyrolysis of waste tires can be further activated to produce activated carbon. This study is based on the chemical activation of waste tire pyrolysis char to produce activated carbon for the removal of lead ions from aqueous solution. This was done by impregnating the waste tire pyrolysis char with Potassium hydroxide and activating it inside a tube furnace under inert conditions to produce waste tire activated carbon. Adsorbent characterisation techniques (SEM, FTIR, TGA, XRF, XRD, BET, and Proximate analysis) were performed on the waste tire pyrolysis char and the activated carbon produced to make a comparison between the two samples. The results showed that the waste tire activated carbon produced has better physical and chemical properties compared to the raw waste tire pyrolysis char. Adsorption results revealed that waste tire activated carbon achieves higher removal percentages of lead ions from aqueous solution compared to waste tire pyrolysis char. The results also showed the effect of various process variables on the adsorption process. Adsorption isotherms, kinetics, and thermodynamics were also studied. The adsorption of lead ions agreed with the Freundlich isotherm model for both the waste tire pyrolysis char and waste tire activated carbon. In terms of adsorption kinetics, the experimental data provided best fits for the pseudo-first order kinetic model for both the waste tire pyrolysis char and the waste tire activated carbon. The adsorption thermodynamics study revealed that the process is an exothermic process and spontaneous in nature. Response surface methodology was used to determine the combined effect of process variables on the adsorption of lead ions onto waste tire activated carbon and to optimise the process using numerical optimisation. The optimum conditions were found to be adsorbent dosage = 1g/100ml, pH = 7, contact time = 115.2 min, initial meta concentration = 100 mg/l, and temperature = 25°C to achieve a maximum adsorption capacity of 93.176 mg/l.

Les relaxations en problème d’optimisation linéaire jouent un rôle central en inférence du maximum a posteriori (map) dans les champs aléatoires de Markov discrets. Nous étudions ici les avantages offerts par les méthodes de Newton pour résoudre efficacement le problème dual (au sens de Lagrange) d’une reformulation lisse du problème. Nous comparons ces dernières aux méthodes de premier ordre, à la fois en terme de vitesse de convergence et de robustesse au mauvais conditionnement du problème. Nous exposons donc un cadre général pour l’apprentissage non-supervisé basé sur le transport optimal et les régularisations parcimonieuses. Nous exhibons notamment une approche prometteuse pour résoudre le problème de la préimage dans l’acp à noyau. Du point de vue de l’optimisation, nous décrivons le calcul du gradient d’une version lisse de la norme p de Schatten et comment cette dernière peut être utilisée dans un schéma de majoration-minimisation. / Numerical optimization and machine learning have had a fruitful relationship, from the perspective of both theory and application. In this thesis, we present an application oriented take on some inference and learning problems. Linear programming relaxations are central to maximum a posteriori (MAP) inference in discrete Markov Random Fields (MRFs). Especially, inference in higher-order MRFs presents challenges in terms of efficiency, scalability and solution quality. In this thesis, we study the benefit of using Newton methods to efficiently optimize the Lagrangian dual of a smooth version of the problem. We investigate their ability to achieve superior convergence behavior and to better handle the ill-conditioned nature of the formulation, as compared to first order methods. We show that it is indeed possible to obtain an efficient trust region Newton method, which uses the true Hessian, for a broad range of MAP inference problems. Given the specific opportunities and challenges in the MAP inference formulation, we present details concerning (i) efficient computation of the Hessian and Hessian-vector products, (ii) a strategy to damp the Newton step that aids efficient and correct optimization, (iii) steps to improve the efficiency of the conjugate gradient method through a truncation rule and a pre-conditioner. We also demonstrate through numerical experiments how a quasi-Newton method could be a good choice for MAP inference in large graphs. MAP inference based on a smooth formulation, could greatly benefit from efficient sum-product computation, which is required for computing the gradient and the Hessian. We show a way to perform sum-product computation for trees with sparse clique potentials. This result could be readily used by other algorithms, also. We show results demonstrating the usefulness of our approach using higher-order MRFs. Then, we discuss potential research topics regarding tightening the LP relaxation and parallel algorithms for MAP inference.Unsupervised learning is an important topic in machine learning and it could potentially help high dimensional problems like inference in graphical models. We show a general framework for unsupervised learning based on optimal transport and sparse regularization. Optimal transport presents interesting challenges from an optimization point of view with its simplex constraints on the rows and columns of the transport plan. We show one way to formulate efficient optimization problems inspired by optimal transport. This could be done by imposing only one set of the simplex constraints and by imposing structure on the transport plan through sparse regularization. We show how unsupervised learning algorithms like exemplar clustering, center based clustering and kernel PCA could fit into this framework based on different forms of regularization. We especially demonstrate a promising approach to address the pre-image problem in kernel PCA. Several methods have been proposed over the years, which generally assume certain types of kernels or have too many hyper-parameters or make restrictive approximations of the underlying geometry. We present a more general method, with only one hyper-parameter to tune and with some interesting geometric properties. From an optimization point of view, we show how to compute the gradient of a smooth version of the Schatten p-norm and how it can be used within a majorization-minimization scheme. Finally, we present results from our various experiments.

This dissertation designs linear transceivers for the multiuser downlink in multiple-input multiple-output (MIMO) systems. The designs rely on an uplink/downlink duality for the mean squared error (MSE) of each individual data stream. We first consider the design of transceivers assuming channel state information (CSI) at the transmitter. We consider minimization of the sum-MSE over all users subject to a sum power constraint on each transmission. Using MSE duality, we solve a computationally simpler convex problem in a virtual uplink. The transformation back to the downlink is simplified by our demonstrating the equality of the optimal power allocations in the uplink and downlink. Our second set of designs maximize the sum throughput for all users. We establish a series of relationships linking MSE to the signal-to-interference-plus-noise ratios of individual data streams and the information theoretic channel capacity under linear minimum MSE decoding. We show that minimizing the product of MSE matrix determinants is equivalent to sum-rate maximization, but we demonstrate that this problem does not admit a computationally efficient solution. We simplify the problem by minimizing the product of mean squared errors (PMSE) and propose an iterative algorithm based on alternating optimization with near-optimal performance. The remainder of the thesis considers the more practical case of imperfections in CSI. First, we consider the impact of delay and limited-rate feedback. We propose a system which employs Kalman prediction to mitigate delay; feedback rate is limited by employing adaptive delta modulation. Next, we consider the robust design of the sum-MSE and PMSE minimizing precoders with delay-free but imperfect estimates of the CSI. We extend the MSE duality to the case of imperfect CSI, and consider a new optimization problem which jointly optimizes the energy allocations for training and data stages along with the sum-MSE/PMSE minimizing transceivers. We prove the separability of these two problems when all users have equal estimation error variances, and propose several techniques to address the more challenging case of unequal estimation errors.

This dissertation designs linear transceivers for the multiuser downlink in multiple-input multiple-output (MIMO) systems. The designs rely on an uplink/downlink duality for the mean squared error (MSE) of each individual data stream. We first consider the design of transceivers assuming channel state information (CSI) at the transmitter. We consider minimization of the sum-MSE over all users subject to a sum power constraint on each transmission. Using MSE duality, we solve a computationally simpler convex problem in a virtual uplink. The transformation back to the downlink is simplified by our demonstrating the equality of the optimal power allocations in the uplink and downlink. Our second set of designs maximize the sum throughput for all users. We establish a series of relationships linking MSE to the signal-to-interference-plus-noise ratios of individual data streams and the information theoretic channel capacity under linear minimum MSE decoding. We show that minimizing the product of MSE matrix determinants is equivalent to sum-rate maximization, but we demonstrate that this problem does not admit a computationally efficient solution. We simplify the problem by minimizing the product of mean squared errors (PMSE) and propose an iterative algorithm based on alternating optimization with near-optimal performance. The remainder of the thesis considers the more practical case of imperfections in CSI. First, we consider the impact of delay and limited-rate feedback. We propose a system which employs Kalman prediction to mitigate delay; feedback rate is limited by employing adaptive delta modulation. Next, we consider the robust design of the sum-MSE and PMSE minimizing precoders with delay-free but imperfect estimates of the CSI. We extend the MSE duality to the case of imperfect CSI, and consider a new optimization problem which jointly optimizes the energy allocations for training and data stages along with the sum-MSE/PMSE minimizing transceivers. We prove the separability of these two problems when all users have equal estimation error variances, and propose several techniques to address the more challenging case of unequal estimation errors.

Au cours des dernières années, s’est développé un intérêt tout particulier pour l’optimisation sans dérivée. Ce domaine de recherche se divise en deux catégories: une déterministe et l’autre stochastique. Bien qu’il s’agisse du même domaine, peu de liens ont déjà été établis entre ces deux branches. Cette thèse a pour objectif de combler cette lacune, en montrant comment les techniques issues de l’optimisation déterministe peuvent améliorer la performance des stratégies évolutionnaires, qui font partie des meilleures méthodes en optimisation stochastique. Sous certaines hypothèses, les modifications réalisées assurent une forme de convergence globale, c’est-à-dire une convergence vers un point stationnaire de premier ordre indépendamment du point de départ choisi. On propose ensuite d’adapter notre algorithme afin qu’il puisse traiter des problèmes avec des contraintes générales. On montrera également comment améliorer les performances numériques des stratégies évolutionnaires en incorporant un pas de recherche au début de chaque itération, dans laquelle on construira alors un modèle quadratique utilisant les points où la fonction coût a déjà été évaluée. Grâce aux récents progrès techniques dans le domaine du calcul parallèle, et à la nature parallélisable des stratégies évolutionnaires, on propose d’appliquer notre algorithme pour résoudre un problème inverse d’imagerie sismique. Les résultats obtenus ont permis d’améliorer la résolution de ce problème. / In recent years, there has been significant and growing interest in Derivative-Free Optimization (DFO). This field can be divided into two categories: deterministic and stochastic. Despite addressing the same problem domain, only few interactions between the two DFO categories were established in the existing literature. In this thesis, we attempt to bridge this gap by showing how ideas from deterministic DFO can improve the efficiency and the rigorousness of one of the most successful class of stochastic algorithms, known as Evolution Strategies (ES’s). We propose to equip a class of ES’s with known techniques from deterministic DFO. The modified ES’s achieve rigorously a form of global convergence under reasonable assumptions. By global convergence, we mean convergence to first-order stationary points independently of the starting point. The modified ES’s are extended to handle general constrained optimization problems. Furthermore, we show how to significantly improve the numerical performance of ES’s by incorporating a search step at the beginning of each iteration. In this step, we build a quadratic model using the points where the objective function has been previously evaluated. Motivated by the recent growth of high performance computing resources and the parallel nature of ES’s, an application of our modified ES’s to Earth imaging Geophysics problem is proposed. The obtained results provide a great improvement for the problem resolution.

Dans ces travaux, nous présentons des méthodes d'optimisation théoriques et numériques pour la conception optimale de circuits magnétiques pour propulseurs à effet Hall. Ces problèmes de conception sont des problèmes inverses très difficiles à résoudre que nous formulons sous forme de problèmes d'optimisation topologique. Les problèmes resultant sont non convexes avec des contraintes aux équations différentielles de Maxwell. Au cours de ces travaux, des approches originales ont été proposées afin de résoudre efficacement ces problèmes d'optimisation topologique. L'approche de densité de matériaux SIMP (Solid Isotropic Material with Penalization) qui est une variante de la méthode d'homogénéisation a été privilégiées. De plus, les travaux de ma thèse ont permis la mise en place de codes d'optimisation dénommé ATOP (Algorithm To Optimize Propulsion) utilisant en parallèle les logiciels de calculs scientifiques Matlab et d'élément finis FEMM (Finite Element Method Magnetics). Dans ATOP, nous utilisant à la fois des algorithmes d'optimisation locale de type descente basés sur une analyse de la sensibilité du problème et des algorithmes d'optimisation globale principalement de type Branch and Bound basés sur l'Arithmétique des Intervals. ATOP permettra d'optimiser à la fois la forme topologique des circuits magnétiques mais aussi le temps et le coût de production de nouvelles génération de propulseurs électriques. / In this work, we present theoretical and numerical optimization method for designing magnetic circuits for Hall effect thrusters. These design problems are very difficult inverse ones that we formulate under the form of topology optimization problems. Then, the obtained problems are non convex subject to Maxwell equations like constraints. Some original approaches have been proposed to solve efficiently these topology optimization problems. These approaches are based on the material density model called SIMP approach (Solid Isotropic Material with Penalization) which is a variante of the homogenization method. The results in my thesis allowed to provide optimization source code named ATOP (Algorithm To Optimize Propulsion) unsung in parallel two scientific computing softwares namely Matlab and FEMM (Finite Element Method Magnetics). In ATOP, we use both local optimization algorithms based on sensitivity analysis of the design problem; and global optimization algorithms mainly of type Branch and Bound based on Interval Arithmetic analysis. ATOP will help to optimize both the topological shape of the magnetic circuits and the time and cost of production (design process) of new generations of electrical thrusters.

Plusieurs machines actuellement utilisées, moteurs à combustion interne en automobile ou centrales thermiques dans l’énergie, rejettent de grandes quantités de chaleur. Généralement cette chaleur est dissipée dans l’atmosphère et son énergie perdue. Nous nous sommes donc intéressés aux moteurs à apport de chaleur externe dont l’énergie primaire est de l’énergie thermique, et plus particulièrement aux moteurs Stirling. L’une de ses principales caractéristiques est d’utiliser de la chaleur produite extérieurement comme source d’énergie. Ceci lui permet d’être multi-carburant et même d’utiliser de l’énergie thermique naturelle.L’étude menée comporte deux parties. Tout d’abord un modèle numérique zéro dimension, trois zones en temps fini a été développé. Il prend en compte les échanges thermiques aux parois et les pertes de charge, mais ne préjuge ni des dimensions moteur, ni des conditions de fonctionnement. Ceci lui permet de rester flexible pour s’adapter à l’architecture spécifique du moteur à simuler. Ensuite nous avons réalisé des mesures expérimentales sur deux moteurs de taille et puissance différentes (quelques watts et 1 kW). Ces résultats ont permis de valider le modèle. Au final nous avons obtenu un modèle numérique traduisant l’influence de paramètres dimensionnels et fonctionnels sur la puissance du moteur Stirling.Un outil d’aide à la conception de moteur Stirling a été développé en ajoutant au modèle un algorithme d’optimisation. Il permet une ébauche des caractéristiques d’un moteur Stirling. En fonction de l’application souhaitée et des contraintes s’y appliquant, il agit sur les caractéristiques choisies par l’utilisateur pour maximiser les performances. / Several machines currently used, internal combustion engines for the car industry or thermal power plants in energy, exhaust a considerable amount of heat. Generally this heat is dispersed in the atmosphere and its energy lost. So we took a special interest in external heat engines which primary energy is heat energy, and more particularly in Stirling engines. One of its main characteristics is the used of energy from heat produced externally like energy source. This allows Stirling engines to be multi-fuel and even to use natural heat energy.The study carried out is made up of two parts. First, a three zones zero dimensional finite-time thermodynamic model has been developed. It takes into account the heat transfer from the walls and the pressure drop, but does not prejudge the dimensions of the engine nor the conditions of its functioning. It is thus able to remain flexible and to adjust to the specific architecture of the engine that should be simulated. Afterwards, we have realized a series of experimental measures thanks to two engines different in size and power (a few Watt and 1 kW). These results allowed us to validate the model. In the end, we got a numerical model representing the influence of dimensional and functional parameters on the power of a Stirling engine.Eventually, a tool to assist in designing Stirling engines was developed adding an optimization algorithm to the model. It allows to sketch out a preliminary draft of the characteristics of a Stirling engine. Depending on the desired application and on the constraints exerted on the engine, the tool created will act on the characteristics of the engine chosen by the user to maximize its performances.