WorldCat Identities

Maréchal, Pierre (1967-....; mathématicien)

Overview
Works: 17 works in 26 publications in 2 languages and 30 library holdings
Roles: Thesis advisor, Other, Opponent
Publication Timeline
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Most widely held works by Pierre Maréchal
Mathématiques appliquées L3 : cours complet avec 500 tests et exercices corrigés by Rémi Abgrall( )

in French and held by 4 WorldCat member libraries worldwide

Progrès en tomographie par synthèse de Fourier by Abdelhadi El Asmai( Book )

2 editions published in 2011 in French and held by 2 WorldCat member libraries worldwide

Tomographic image reconstruction is used to visualize 3D distribution of a radiopharmaceutical inside a patient's body from a series of 2D images taken under various incidences. In these last years significant progress were obtained by taking into account more realistic model of image acquisition system, which includes in particular the impulse response of the camera and other factors of image degradation. However, from a mathematical viewpoint the problem is an ill-posed inverse problem. In this thesis we considered a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to the Fourier synthesis. It refines previous contributions, in which the preprocessing of the data was performed according to the Fourier slice theorem. Since real models must account for the geometrical system response and possibly Compton scattering and attenuation, The Fourier slice theorem does not apply, yielding redefinition of the preprocessing. In general, the latter is not explicit, and must be performed numerically. The most natural choice of preprocessing involves the computation of unstable solutions. A proximal strategy is proposed for this step, which allows for accurate computations and preserves global stability of the reconstruction process
Optimisation du réseau de routes en zone terminale by Man Liang( Book )

2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide

La congestion dans les Terminal Manoeuvring Area (TMA) des aéroports en hub est le principal problème dans le transport aérien chinois. Face au trafic extrêmement dense dans les TMAs, nous pouvons envisager d'automatiser une grande partie des opérations de routine, comprenant la planification, le séquencement et la séparation. Nous proposons dans cette thèse un nouveau système automatisé de séquencement des avions et de fusion des flux vers des pistes parallèles, qui sont utilisées dans la plupart des aéroports chinois. Notre méthodologie intègre un réseau de route 3D nommé Multi-Level and Multi-Point Merge System (MLMPMS) basé sur le concept de l'Area Navigation (RNAV) et un algorithme d'optimisation heuristique hybride pour trouver une solution correcte, opérationnellement acceptable. Un algorithme de Simulated Annealing (SA) spécifique et un module de génération de trajectoire collaborent pour rechercher la solution quasi optimale. Notre objectif est de générer en temps réel des trajectoires sans conflit, minimisant la consommation de carburant et permettant des méthodes de contrôle faciles et flexibles. Dans ce but, nous explorons en permanence les solutions possibles avec le moins de retard et assuront l'atterrissage le plus rapide. Nous déterminons quatre variables de décision pour contrôler chaque vol : l'heure et la vitesse d'entrée dans la TMA, le temps de vol sur l'arc de séquencement et le choix de la piste utilisée. La simulation de trajectoire dans les différentes phases de vol est basée sur le modèle de performances BADA. Dans le cas de l'aéroport de Beijing Capital International Airport (BCIA), les résultats numériques montrent que notre système d'optimisation de bonnes performances sur le séquencement et la fusion des trajectoires. Tout d'abord, il permet d'assurer des performances de résolution conflit très stables pour gérer les flux de trafic continuellement denses. Par rapport à l'algorithme Hill Climbing (HC), le SA peut toujours trouver une solution sans conflit, non seulement pour l'approche parallèle mixte ou séparée~(pour les arrivées), mais aussi pour les configurations parallèles indépendantes~ (départs et arrivées intégrés). Ensuite, avec un réseau d'itinéraires Multi-Level Point Merge (ML-PM) unique, il peut fournir une bonne solution de contrôle de la trajectoire pour traiter efficacement et économiquement différents types de flux d'arrivée. Il peut réaliser un temps de vol plus court et une descente vers le bas en Continuous Descent Approach (CDA) pour l'avion d'arrivée. Il peut réaliser un re-séquencement plus facile des avions avec un déplacement de position plus relâché. Théoriquement, les Maximum Position Shifting (MPS) peuvent atteindre 6 positions, surpassant la contrainte difficile de 3 positions. Troisièmement, l'algorithme montre son efficacité dans un modèle d'approche parallèle séparé avec une capacité de séquencement plus relâché. Par rapport au décalage de position forcé dur, qui est souvent utilisé dans le système actuel Arrival Manager (AMAN) et la méthode First Come First Served (FCFS) utilisé par les contrôleurs, il peut réduire le délai et le temps de transit moyens dans une situation d'arrivée très dense. Le palier par vol est inférieur à 12\% du temps de transit total dans la TMA. Quatrièmement, en configuration parallèle indépendant, il peut fournir des informations différentes concernant la valeur objectif associée, le temps de vol moyen, les trajectoires de croisement en point chaud entre les arrivées et les départs, l'efficacité avec différents arcs de séquencement conçus dans le réseau de route ML-PM etc
A Note on the Morozov Principle via Lagrange Duality by Xavier Bonnefond( )

1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide

Optimisation des routes de départ et d'arrivée aux approches des grands aéroports by Jérémie Chevalier( Book )

2 editions published in 2020 in English and held by 2 WorldCat member libraries worldwide

The bottleneck of today's airspace is the Terminal Maneuvering Areas (TMA), where aircraft leave their routes to descend to an airport or take off and reach the en-route sector. To avoid congestion in these areas, an efficient design of departure and arrival routes is necessary. In this work, a solution for designing departure and arrival routes is proposed, which takes into account the runway configuration, the surroundings of the airport and operational constraints such as limited slopes or turn angles. The routes consist of two parts: a horizontal path in a graph constructed by sampling the TMA around the runway, to which is associated a cone of altitudes. The set of all routes is optimized by the Simulated Annealing metaheuristic. In the process and at each iteration, each route is computed by defining adequately the cost of the arcs in the graph and then searching a path on it. The costs are chosen so as to avoid zigzag behaviors as much as possible. Several tests were performed, one on an artificial problem designed specifically to test this approach and the three others on instances taken from the literature. The obtained results are satisfying with regard to the current state of air operations management and constraints
Implémentations d'optimisation-simulation pour l'harmonisation des opérations dans les grands aéroports by Paolo Maria Scala( Book )

2 editions published in 2019 in French and held by 2 WorldCat member libraries worldwide

The constant growth of air traffic, especially in Europe, is putting pressure on airports, which, in turn, are suffering congestion problems. The airspace surrounding airport, terminal manoeuvring area (TMA), is particularly congested, since it accommodates all the converging traffic to and from airports. Besides airspace, airport ground capacity is also facing congestion problems, as the inefficiencies coming from airspace operations are transferred to airport ground and vice versa. The main consequences of congestion at airport airspace and ground, is given by the amount of delay generated, which is, in turn, transferred to other airports within the network. Congestion problems affect also the workload of air traffic controllers that need to handle this big amount of traffic. This thesis deals with the optimization of the integrated airport operations, considering the airport from a holistic point of view, by including operations such as airspace and ground together. Unlike other studies in this field of research, this thesis contributes by supporting the decisions of air traffic controllers regarding aircraft sequencing and by mitigating congestion on the airport ground area. The airport ground operations and airspace operations can be tackled with two different levels of abstractions, macroscopic or microscopic, based on the time-frame for decision-making purposes. In this thesis, the airport operations are modeled at a macroscopic level. The problem is formulated as an optimization model by identifying an objective function that considers the amount of conflicts in the airspace and capacity overload on the airport ground; constraints given by regulations on separation minima between consecutive aircraft in the airspace and on the runway; decision variables related to aircraft entry time and entry speed in the airspace, landing runway and departing runway choice and pushback time. The optimization model is solved by implementing a sliding window approach and an adapted version of the metaheuristic simulated annealing. Uncertainty is included in the operations by developing a simulation model and by including stochastic variables that represent the most significant sources of uncertainty when considering operations at a macroscopic level, such as deviation from the entry time in the airspace, deviation in the average taxi time and deviation in the pushback time
Contributions à la tomographie thermoacoustique : modélisation et inversion by Xavier Bonnefond( Book )

2 editions published in 2010 in French and held by 2 WorldCat member libraries worldwide

ThermoAcoustic Tomography (TAT) is a medical imaging technique using the pressure wave generated by a body illuminated by an electromagnetic pulse. Since the acoustic signal is recorded around the body, the resulting inverse problem can be formulated as follows : from the knowledge of a solution of the wave equation on some hypersurface, reconstruct its initial condition. Despite several inversion formulas, so far no efficient procedure, taking partial data and damping into account, is known. As well as a state of the art, this work is dedicated to the introduction of a variational approach for the TAT problem. We studied the regularization by mollification, which consists in replacing the original object by a limited resolution version of it, and treating the data so that they fit this new objective. Moreover, we used a noise level estimation provided by the Golub-Kahan bidiagonalization process to allow an accurate regularization parameter selection. In the second part of this work, we investigate the usual TAT model and put forward some damped wave equation with a finite wave front speed. This improvement yields to the use of the Back and Forth Nudging (BFN) method, which was first implemented for data assimilation purposes, to invert the TAT problem. This technique provides a sequence of approximations of the solution by iterating forward and backward implementations of a wave equation including a newtonian recall to the data. This method, which is proved to be convergent in an ideal framework, leads to convincing results in both partial data and attenuated wave cases
Modelling fatigue spectra of aircraft structure under gust loads by Thomas Reytier( Book )

2 editions published in 2012 in English and held by 2 WorldCat member libraries worldwide

This thesis is dedicated to the fatigue and damage tolerance analysis of the aircraft structures under gust loads. The fatigue and damage tolerance analysis is a significant issue in the aircraft structure design. It aims at defining the inspection program of the aircraft structure in order to ensure its safety through its entire life. The first part reviews the state-of-the-art in the various involved topics for the global process for fatigue analysis of aircraft structure under gust loads: the atmospheric turbulence modelling, the load and stress computation by a finite element analysis, the generation of the fatigue spectrum and at the end, the fatigue and damage tolerance analysis. The second part presents the whole process currently implemented at Airbus. The main strengths and weaknesses are pointed out and this en-ables the identification of several improvement axes. From the continuous turbulence model based on the Von Karman Power Spectral Density(PSD), the computed stresses are included according to statistics established from in-flight measurements in the fatigue spectrum in order to build a stress cycle sequence. The input data for the fatigue and damage tolerance analysis are obtained from the definition of the various fatigue mission profiles, the unitary stress values, the dynamic response of the structure and the turbulence statistics. In the third part,a new methodology is presented in order to obtaine efficiently and accurately the temporal stress sequences due to the atmospheric turbulence. This method relies on new results enabling the generation of correlated time signals from the PSD functions. First, the PSD of the various stress components are directly obtained from the Von Karman PSD via a finite element analysis. Then, the correlated temporal stress sequences are generated and distributed in the fatigue spectrum according to the turbulence intensity statistical law. This new process enables the improvement of the stress computation and the fatigue spectrum generation. It replaces the turbulence statistics by stress exceedance statistics which are defined by an analytical formula in a reasonably conservative way. In addition, the lead time to build the input data for the fatigue and damage tolerance analysis is significantly reduced. Results from the fatigue and damage tolerance analysis are presented in order to highlight the quality of the improved processes both in terms of accuracy and lead time
Méthode de Monte-Carlo et non-linéarités : de la physique du transfert radiatif à la cinétique des gaz by Guillaume Terrée( Book )

2 editions published in 2015 in French and held by 2 WorldCat member libraries worldwide

In transport physics, especially in radiative transfer physics, the Monte-Carlo method has been originally developed as the simulation of the history of numerous particles, from which are deduced mean observables. This numerical method owes its success to several qualities : a natural management of many-dimensional phase space, a null systematic error away from the mathematical and physical model, the confidence intervals given with the results, an ability to take into account simultaneously numerous physical phenomenons, the simultaneous sensitivities calculating possibility, and an easy parallelization. In gas kinetics, particles collide each other, not with an external fixed medium ; it is said that their transport is non-linear. These mutual collisions put out of action the aforesaid approach of the Monte-Carlo method ; because in order to simulate the independent trajectories of multiple particles and thus estimate their distribution, this distribution must beforehand be exactly known...This thesis follows on from those of Jérémy DAUCHET (2012) and of Mathieu GALTIER (2014), dedicated to radiative transfer physics. Between other works, these authors have shown how the Monte-Carlo method can bear non-linearities, while keeping its customary formalism and specificities. The then overcome non-linearities were respectively a chemistry/irradiance coupling law, and the dependence of the irradiance toward the absorption coefficient. We try in this manuscript to overcome the non-linearity of the transport. In this aim, our main tools are a reverse following of particles, based on integral formulations of the transport equations, formulations largely inspired from the so-called null collisions algorithms. We show, on several academic examples, that we have indeed extended the Monte Carlo method to the resolution of the Boltzmann equation. These examples are also occasions to test the limits of what we have built. The most noteworthy results are certainly the absence of any mesh in the numerical method, and its capacity to calculate correctly the high-speed particles quantities (always rare compared to the total, in gas kinetics). Beyond the given examples, this manuscript is wanted as a formalism attempt and an exploration of the developed method basics. The focus is made on the reasoning leading to the method, rather than on particular implementations which have been realized. In the eyes of the author, the method is still largely reworkable. In particular, the maximal times on which the evolution of particles is computable, which constitute the main weakness of the developed numerical method, can surely be increased
Classification en espaces fonctionnels utilisant la norme BV avec applications aux images ophtalmologiques et à la complexité du trafic aérien by Bang Giang Nguyen( Book )

2 editions published between 2014 and 2015 in English and held by 2 WorldCat member libraries worldwide

In this thesis, we deal with two different problems using Total Variation concept. The first problem concerns the classification of vasculitis in multiple sclerosis fundus angiography, aiming to help ophthalmologists to diagnose such autoimmune diseases. It also aims at determining potential angiography details in intermediate uveitis in order to help diagnosing multiple sclerosis. The second problem aims at developing new airspace congestion metric, which is an important index that is used for improving Air Traffic Management (ATM) capacity. In the first part of this thesis, we provide preliminary knowledge required to solve the above-mentioned problems. First, we present an overview of the Total Variation and express how it is used in our methods. Then, we present a tutorial on Support Vector Machines (SVMs) which is a learning algorithm used for classification and regression. In the second part of this thesis, we first provide a review of methods for segmentation and measurement of blood vessel in retinal image that is an important step in our method. Then, we present our proposed method for classification of retinal images. First, we detect the diseased region in the pathological images based on the computation of BV norm at each point along the centerline of the blood vessels. Then, to classify the images, we introduce a feature extraction strategy to generate a set of feature vectors that represents the input image set for the SVMs. After that, a standard SVM classifier is applied in order to classify the images. Finally, in the third part of this thesis, we address two applications of TV in the ATM domain. In the first application, based on the ideas developed in the second part, we introduce a methodology to extract the main air traffic flows in the airspace. Moreover, we develop a new airspace complexity indicator which can be used to organize air traffic at macroscopic level. This indicator is then compared to the regular density metric which is computed just by counting the number of aircraft in the airspace sector. The second application is based on a dynamical system model of air traffic. We propose a method for developing a new traffic complexity metric by computing the local vectorial total variation norm of the relative deviation vector field. Its aim is to reduce complexity. Three different traffic situations are investigated to evaluate the fitness of the proposed method
On the variational approach to mollification in the theory of ill-posed problems and applications by Walter Cédric Simo Tao Lee( Book )

2 editions published in 2020 in French and held by 2 WorldCat member libraries worldwide

Les problèmes inverses constituent un domaine en pleine expansion en mathématiques appliquées qui a suscité une grande attention au cours des dernières décennies en raison de son omniprésence dans plusieurs domaines des sciences et technologies. Le plus souvent, les problèmes inverses donnent lieu à des équations mathématiques instables. Autrement dit, les solutions ne dépendent pas continument des données. En effet, de très petites perturbations sur les données peuvent causer des erreurs arbitrairement grandes sur les solutions. Étant donné que le bruit est généralement inévitable, inverser l'équation mal-posée échoue à résoudre le problème. Il est alors nécessaire d'appliquer une méthode de régularisation afin de récupérer des approximations stables des solutions. À cet égard, plusieurs techniques de régularisation ont été développées dans la littérature. Globalement, ces méthodes de régularisation peuvent être divisées en deux classes : Une classe de méthodes qui tentent de reconstruire les solutions inconnues initiales et une classe de méthodes qui tentent de reconstruire des versions lisses des solutions inconnues. L'objectif de cette thèse est de contribuer à la promotion de la deuxième classe de méthode de régularisation à travers l'étude et l'application de la formulation variationnelle de la mollification. Dans ce manuscrit, nous montrons que l'approche variationnelle de la mollification peut être étendue à la régularisation de problèmes mal-posés impliquant des opérateurs non compacts. À cet égard, nous étudions et appliquons avec succès la méthode à la régression instrumentale non-paramétrique. Une contribution supplémentaire de cette thèse est la conception et l'étude d'une nouvelle méthode de régularisation adaptée aux problèmes linéaires exponentiellement mal-posés. Une comparaison numérique de cette nouvelle méthode aux méthodes classiques de régularisation telles que Tikhonov, la spectral cut-off, la régularisation asymptotique et la méthode des gradients conjugués est effectuée sur trois problèmes test tirés de la littérature. L'aspect pratique de la sélection du paramètre de régularisation avec un niveau de bruit inconnu est également considéré. Outre l'étude et l'application des méthodes de régularisation, cette thèse traite également de l'application d'une règle de sélection de paramètres de régularisation très populaire connue sous le nom du principe de Morozov. En utilisant la dualité de Lagrange, nous fournissons un algorithme simple et rapide pour le calcul du paramètre de régularisation correspondant à cette règle pour les méthodes de régularisation du type Tikhonov. L'intérêt de cette étude est qu'elle met en avant une méthode de régularisation mal connue qui pourtant a un grand potentiel et est capable de fournir des solutions approchées comparativement meilleures que certaines techniques de régularisation classiques bien connues. Un autre apport de cette thèse est la conception d'une nouvelle méthode de régularisation qui, selon nous, est prometteuse dans la régularisation de problèmes exponentiellement mal-posés, en particulier pour les problèmes inverses de conduction thermique
Contributions à la tomographie thermoacoustique modélisation et inversion by Xavier Bonnefond( )

1 edition published in 2011 in French and held by 1 WorldCat member library worldwide

La Tomographie ThermoAcoustique (TTA) est une technique d'imagerie médicale où un corps exposé à une impulsion électromagnétique génère une onde acoustique mesurée autour de celui-ci. Le modèle établi pour la TTA conduit au problème inverse suivant : étant connue la solution d'une équation des ondes sur une hypersurface, il s'agit de reconstruire sa condition initiale. Malgré l'existence de formules explicites, aucune procédure d'inversion rapide, stable et valable en situation clinique n'existe à ce jour. Outre une synthèse des travaux existants, l'objet de ce travail a été, dans un premier temps, d'élaborer une approche variationnelle pour le problème de la TTA. Nous avons considéré la régularisation par mollification, où l'objet à reconstruire est remplacé par une version à résolution limitée, tandis que les données sont traitées pour plus de cohérence. De plus, une stratégie de sélection de paramètre de régularisation utilisant les méthodes de Krylov, et valable pour les régularisations de type Tikhonov, est proposée. Dans un deuxième temps, le modèle usuel de la TTA a été remis en question afin de prendre en compte l'atténuation subie en pratique par l'onde mesurée. On propose plusieurs équations des ondes atténuées causales. Cette évolution du modèle nous a conduit à tester la méthode du Back and Forth Nudging (BFN), issue du champ de l'assimilation de données, consistant à introduire un rappel aux données newtonien dans l'équation des ondes, puis à alterner des résolutions en temps direct et rétrograde. La convergence de la méthode est démontrée dans un cas idéal, mais le procédé offre d'excellents résultats en situation de données incomplètes et atténuées
Approche novatrice pour la conception et l'exploitation d'avions écologiques by Sylvain Prigent( )

1 edition published in 2015 in English and held by 1 WorldCat member library worldwide

The objective of this PhD work is to pose, investigate, and solve the highly multidisciplinary and multiobjective problem of environmentally efficient aircraft design and operation. In this purpose, the main three drivers for optimizing the environmental performance of an aircraft are the airframe, the engine, and the mission profiles. The figures of merit, which will be considered for optimization, are fuel burn, local emissions, global emissions, and climate impact (noise excluded). The study will be focused on finding efficient compromise strategies and identifying the most powerful design architectures and design driver combinations for improvement of environmental performances. The modeling uncertainty will be considered thanks to rigorously selected methods. A hybrid aircraft configuration is proposed to reach the climatic impact reduction objective
Progrès en tomographie par synthèse de Fourier by Abdelhadi El Asmai( )

1 edition published in 2012 in French and held by 1 WorldCat member library worldwide

Tomographic image reconstruction is used to visualize 3D distribution of a radiopharmaceutical inside a patient's body from a series of 2D images taken under various incidences. In these last years significant progress were obtained by taking into account more realistic model of image acquisition system, which includes in particular the impulse response of the camera and other factors of image degradation. However, from a mathematical viewpoint the problem is an ill-posed inverse problem. In this thesis we considered a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to the Fourier synthesis. It refines previous contributions, in which the preprocessing of the data was performed according to the Fourier slice theorem. Since real models must account for the geometrical system response and possibly Compton scattering and attenuation, The Fourier slice theorem does not apply, yielding redefinition of the preprocessing. In general, the latter is not explicit, and must be performed numerically. The most natural choice of preprocessing involves the computation of unstable solutions. A proximal strategy is proposed for this step, which allows for accurate computations and preserves global stability of the reconstruction process
Modelling fatigue spectra of aircraft structure under gust loads by Thomas Reytier( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

This thesis is dedicated to the fatigue and damage tolerance analysis of the aircraft structures under gust loads. The fatigue and damage tolerance analysis is a significant issue in the aircraft structure design. It aims at defining the inspection program of the aircraft structure in order to ensure its safety through its entire life. The first part reviews the state-of-the-art in the various involved topics for the global process for fatigue analysis of aircraft structure under gust loads: the atmospheric turbulence modelling, the load and stress computation by a finite element analysis, the generation of the fatigue spectrum and at the end, the fatigue and damage tolerance analysis. The second part presents the whole process currently implemented at Airbus. The main strengths and weaknesses are pointed out and this en-ables the identification of several improvement axes. From the continuous turbulence model based on the Von Karman Power Spectral Density(PSD), the computed stresses are included according to statistics established from in-flight measurements in the fatigue spectrum in order to build a stress cycle sequence. The input data for the fatigue and damage tolerance analysis are obtained from the definition of the various fatigue mission profiles, the unitary stress values, the dynamic response of the structure and the turbulence statistics. In the third part,a new methodology is presented in order to obtaine efficiently and accurately the temporal stress sequences due to the atmospheric turbulence. This method relies on new results enabling the generation of correlated time signals from the PSD functions. First, the PSD of the various stress components are directly obtained from the Von Karman PSD via a finite element analysis. Then, the correlated temporal stress sequences are generated and distributed in the fatigue spectrum according to the turbulence intensity statistical law. This new process enables the improvement of the stress computation and the fatigue spectrum generation. It replaces the turbulence statistics by stress exceedance statistics which are defined by an analytical formula in a reasonably conservative way. In addition, the lead time to build the input data for the fatigue and damage tolerance analysis is significantly reduced. Results from the fatigue and damage tolerance analysis are presented in order to highlight the quality of the improved processes both in terms of accuracy and lead time
Quelques contributions aux problèmes inverses de synthèse de Fourier by Yaowaluk Saesor( Book )

in English and held by 1 WorldCat member library worldwide

Approches basées sur DCA pour la programmation mathématique avec des contraintes d'équilibre by Thi Minh Tam Nguyen( )

1 edition published in 2018 in English and held by 1 WorldCat member library worldwide

In this dissertation, we investigate approaches based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for mathematical programs with equilibrium constraints. Being a classical and challenging topic of nonconvex optimization, and because of its many important applications, mathematical programming with equilibrium constraints has attracted the attention of many researchers since many years. The dissertation consists of four main chapters. Chapter 2 studies a class of mathematical programs with linear complementarity constraints. By using four penalty functions, we reformulate the considered problem as standard DC programs, i.e. minimizing a DC function on a convex set. The appropriate DCA schemes are developed to solve these four DC programs. Two among them are reformulated again as general DC programs (i.e. minimizing a DC function under DC constraints) in order that the convex subproblems in DCA are easier to solve. After designing DCA for the considered problem, we show how to develop these DCA schemes for solving the quadratic problem with linear complementarity constraints and the asymmetric eigenvalue complementarity problem. Chapter 3 addresses a class of mathematical programs with variational inequality constraints. We use a penalty technique to recast the considered problem as a DC program. A variant of DCA and its accelerated version are proposed to solve this DC program. As an application, we tackle the second-best toll pricing problem with fixed demands. Chapter 4 focuses on a class of bilevel optimization problems with binary upper level variables. By using an exact penalty function, we express the bilevel problem as a standard DC program for which an efficient DCA scheme is developed. We apply the proposed algorithm to solve a maximum flow network interdiction problem. In chapter 5, we are interested in the continuous equilibrium network design problem. It was formulated as a Mathematical Program with Complementarity Constraints (MPCC). We reformulate this MPCC problem as a general DC program and then propose a suitable DCA scheme for the resulting problem
 
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