Auswahl der wissenschaftlichen Literatur zum Thema „SDP optimization“

We propose two multigrid approaches for the global optimization of polynomial op- timization problems. In our first contribution we consider problems that arise from the discretization of infinite dimensional optimization problems, such as PDE optimiza- tion problems, boundary value problems and some global optimization applications. In many of these applications, the level of discretization can be used to obtain a hierarchy of optimization models that captures the underlying infinite dimensional problem at different degrees of fidelity. This approach, inspired by multigrid methods, has been successfully used for decades to solve large systems of linear equations. However, it has not been adapted to SDP relaxations of polynomial optimization problems. The main difficulty is that the geometric information between grids is lost when the original problem is approximated via an SDP relaxation. Despite the loss of geometric infor- mation, we show how a multigrid approach can be applied by developing prolongation operators to relate the primal and dual variables of the SDP relaxation between lower and higher levels in the hierarchy of discretizations. We develop sufficient conditions for the operators to be useful in applications. Our conditions are easy to verify in prac- tice, and we discuss how they can be used to reduce the complexity of infeasible interior iv point methods. Following the same reasoning, the second approach does not assume any particular structure of the underlying polynomial problem, but instead considers the hierarchy of sparse SDP relaxations that can be obtained for any unconstrained polynomial optimizations problem with structured sparsity. Prolongation operators are defined for this type of hierarchy, and theoretical results that show their usefulness are proved. Our preliminary results highlight two promising advantages of following a multigrid approach in contrast with a pure interior point method: the percentage of problems that can be solved to a high accuracy is much higher, and the time necessary to find a solution can be reduced significantly, especially for large scale problems.

Dans la première partie de cette thèse, nous utilisons l'algorithme d'Expectation-Maximization (EM) pour estimer en aveugle les amplitudes des coefficients du canal, et nous comparons les résultats avec la borne de Cramer-Rao. De plus, nous développons une version relaxe de la détection MV, à faible complexité et montrons que ses performances surpassent celles du détecteur d'erreur quadratique moyenne minimale (EQMM). La deuxième partie de cette thèse concerne le problème de la détection dans les systèmes MEMS. Nous proposerons un algorithme de détection MV utilisant une approche géométrique discrète. L'avantage de cet algorithme est sa complexité polynomiale, quel que soit le rapport signal-bruit, et le fait qu'aucune méthode heuristique n'est employé. Nous obtenons une méthode MV approches a faible complexité par l'approche de la programmation en cone du deuxième ordre. Nous établissons également des bornes sur la performance de la méthode de programmation semi-definie. Jusqu'ici, la connaissance de l'état du canal était considéré comme parfaite. Nous avons également explore le problème de la détection sans connaissance du canal au récepteur. Le résultat est un algorithme d'estimation conjointe du canal et des symboles, base sur l'algorithme EM, et la théorie du champ dynamique moyen (CDM, ou mean field theory, méthode largement utilise en physique statistique) pour en réduire la complexité L'approche du CDM est utilise pour approximer les probabilité {\em a posteriori} d'interférence d'access multiple. Les performances de la méthode propose sont compares a celles du détecteur MV exact pour un canal connu<br>We focus on low complexity maximum likelihood detection. The em algorithm is a broadly applicable approach to the iterative computation of ml estimates, useful in variety of incomplete-data problems, where algorithms such as the newton-raphson method may turn out to be more complicated. In the first part of the thesis, we use em algorithm to estimate the channel amplitudes blindly and compare the results with the cramer-rao bound (crb). The second part of the thesis concerns the detection problem in mimo systems. We are able to device an algorithm for approximate ml detection using a discrete geometric approach. The advantage of this algorithm is that its performance is polynomial irrespective of the snr and no heuristic is employed in our algorithm. An alternative way to ml problem is to devise low complexity algorithms whose performance is close to the exact ml. This can be done using semidefinite programming (sdp) approach. The computational complexity of the sdp approach is comparable to the average complexity of the sphere decoder but still it is quite complicated for large systems. We obtained low complexity (by reducing the number of the variables) approximate ml by second order cone programming (socp) approach. In the above discussion the channel state information is assumed to be known at the receiver. We further looked into the problem of detection with no channel knowledge at the receiver. The result was the joint channel-symbol estimation. We obtained the results of joint channel-symbol estimation using em algorithm and in order to reduce the complexity of the resulting em algorithm, we used mean field theory (mft) approach

We apply the semidefinite programming method to obtain a new upper bound on the cardinality of codes made of subspaces of a linear vector space over a finite field. Such codes are of interest in network coding.Next, with the same method, we prove an upper bound on the cardinality of sets avoiding one distance in the Johnson space, which is essentially Schrijver semidefinite program. This bound is used to improve existing results on the measurable chromatic number of the Euclidean space.We build a new hierarchy of semidefinite programs whose optimal values give upper bounds on the independence number of a graph. This hierarchy is based on matrices arising from simplicial complexes. We show some properties that our hierarchy shares with other classical ones. As an example, we show its application to the problem of determining the independence number of Paley graphs.

L'objectif de cette thèse porte sur des recherches théoriques et algorithmiques d'optimisation locale et globale via les techniques de programmation DC & DCA, Séparation et Evaluation (SE) ainsi que les techniques de relaxation DC/SDP, pour résoudre plusieurs types de problèmes d'optimisation non convexe (notamment en Optimisation Combinatoire et Optimisation Polynomiale). La thèse comporte quatre parties :La première partie présente les outils fondamentaux et les techniques essentielles en programmation DC & l'Algorithme DC (DCA), ainsi que les techniques de relaxation SDP, et les méthodes de séparation et évaluation (SE).Dans la deuxième partie, nous nous intéressons à la résolution de problèmes de programmation quadratique et linéaire mixte en variables entières. Nous proposons de nouvelles approches locales et globales basées sur DCA, SE et SDP. L'implémentation de logiciel et des simulations numériques sont aussi étudiées.La troisième partie explore des approches de la programmation DC & DCA en les combinant aux techniques SE et SDP pour la résolution locale et globale de programmes polynomiaux. Le programme polynomial avec des fonctions polynomiales homogènes et son application à la gestion de portefeuille avec moments d'ordre supérieur en optimisation financière ont été discutés de manière approfondie dans cette partie.Enfin, nous étudions dans la dernière partie un programme d'optimisation sous contraintes de type matrices semi-définies via nos approches de la programmation DC. Nous nous consacrons à la résolution du problème de réalisabilité des contraintes BMI et QMI en contrôle optimal.L'ensemble de ces travaux a été implémenté avec MATLAB, C/C++ ... nous permettant de confirmer l'utilisation pratique et d'enrichir nos travaux de recherche.

This dissertation develops efficient solution techniques for general and problem-specific applications within nonconvex optimization, exploiting the constructs of the Reformulation-Linearization Technique (RLT). We begin by developing a technique to enhance general problems in nonconvex optimization through the use of a new class of RLT cuts, called semidefinite cuts. While these cuts are valid for any general problem for which RLT is applicable, we demonstrate their effectiveness in optimizing a nonconvex quadratic objective function over a simplex. Computational results indicate that on average, the semidefinite cuts have reduced the number of nodes in the branch-and-bound tree by a factor of 37.6, while decreasing solution time by a factor of 3.4. The semidefinite cuts have also led to a significant reduction in the optimality gap at termination, in some cases producing optimal solutions for problems that could not be solved using RLT alone. We then narrow our focus to the class of mixed-integer programming (MIP) problems, and develop a modification of Bendersâ decomposition method using concepts from RLT and lift-and-project cuts. This method is particularly motivated by the class of two-stage stochastic programs with integer recourse. The key idea is to design an RLT or lift-and-project cutting plane scheme for solving the subproblems where the cuts generated have right-hand sides that are functions of the first-stage variables. An illustrative example is provided to elucidate the proposed approach. The focus is on developing a first comprehensive finitely convergent extension of Bendersâ methodology for problems having 0-1 mixed-integer subproblems. We next address a specific challenging MIP application known as the facility layout problem, and we significantly improve its formulation through outer-linearization techniques and concepts from disjunctive programming. The enhancements produce a substantial increase in the accuracy of the layout produced, while at the same time, providing a dramatic reduction in computational effort. Overall, the maximum error in department size was reduced from about 6% to nearly zero, while solution time decreased by a factor of 110. Previously unsolved test problems from the literature that had defied even approximate solution methods have been solved to exact optimality using our proposed approach.<br>Ph. D.

The Energy Management Strategy (EMS) has a huge effect on the performance of any hybrid vehicle because it determines the operating point of almost every component associated with the powertrain. This means that its optimisation is an incredibly complex task which must consider a number of objectives including the fuel consumption, drive-ability, component degradation and straight-line performance. The EMS is of particular importance for Fuel Cell Hybrid Electric Vehicles (FCHEVs), not only to minimise the fuel consumption, but also to reduce the electrical stress on the fuel cell and maximise its useful lifetime. This is because the durability and cost of the fuel cell stack is one of the major obstacles preventing FCHEVs from being competitive with conventional vehicles. In this work, a novel EMS is developed, specifcally for Fuel Cell Hybrid Electric Vehicles (FCHEVs), which considers not only the fuel consumption, but also the degradation of the fuel cell in order to optimise the overall running cost of the vehicle. This work is believed to be the first of its kind to quantify effect of decisions made by the EMS on the fuel cell degradation, inclusive of multiple causes of voltage degradation. The performance of this new strategy is compared in simulation to a recent strategy from the literature designed solely to optimise the fuel consumption. It is found that the inclusion of the degradation metrics results in a 20% increase in fuel cell lifetime for only a 3.7% increase in the fuel consumption, meaning that the overall running cost is reduced by 9%. In addition to direct implementation on board a vehicle, this technique for optimising the degradation alongside the fuel consumption also allows alternative vehicle designs to be compared in an unbiased way. In order to demonstrate this, the novel optimisation technique is subsequently used to compare alternative system designs in order to identify the optimal economic sizing of the fuel cell and battery pack. It is found that the overall running cost can be minimised by using the smallest possible fuel cell stack that will satisfy the average power requirement of the duty cycle, and by using an oversized battery pack to maximise the fuel cell effciency and minimise the transient loading on the stack. This research was undertaken at Loughborough University as part of the Doctoral Training Centre (DTC) in Hydrogen, Fuel Cells and Their Applications in collaboration with the University of Birmingham and Nottingham University and with sponsorship from HORIBA-MIRA (Nuneaton, UK). A Microcab H4 test vehicle has been made available for use in testing for this research which was previously used for approximately 2 years at the University of Birmingham. The Microcab H4 is a small campus based vehicle designed for passenger transport and mail delivery at low speeds as seen on a university campus. It has a top speed of approximately 30mph, and is fitted with a 1.2kW fuel cell and a 2kWh battery pack.

Les robots flexibles sont de plus en plus utilisés dans les applications pratiques. Ces robots sont caractérisés par une conception mécanique légère, réduisant ainsi leur encombrement, leur consommation d'énergie et améliorant leur sécurité. Cependant, la présence de vibrations transitoires rend difficile un contrôle précis de la trajectoire de ces systèmes. Cette thèse est précisément consacrée à l'asservissement en position des manipulateurs flexibles dans les espaces articulaire et opérationnel. Des méthodes de commande avancées, basées sur des outils de la commande robuste et de l'optimisation convexe, ont été proposées. Ces méthodes font en particulier appel à la théorie des systèmes linéaires à paramètres variants (LPV) et aux inégalités matricielles linéaires (LMI). En comparaison avec des lois de commande non-linéaires disponibles dans la littérature, les lois de commande LPV proposées permettent de considérerdes contraintes de performance et de robustesse de manière simple et systématique. L'accent est porté dans notre travail sur la gestion appropriée de la dépendance paramétrique du modèle LPV, en particulier les dépendances polynomiale et rationnelle. Des simulations numériques effectuées dans des conditions réalistes, ont permis d'observer une meilleure robustesse de la commande LPV par rapport à la commande non-linéaire par inversion de modèle face aux bruits de mesure, aux excitations de haute fréquence et aux incertitudes de modèle.

Nowadays in the world of mass consumption there is big demand for distributioncenters of bigger size. Managing such a center is a very complex and difficult taskregarding to the different processes and factors in a usual warehouse when we want tominimize the labor costs. Most of the workers’ working time is spent with travelingbetween source and destination points which cause deadheading. Even if a worker knowsthe structure of a warehouse well and because of that he or she can find the shortest pathbetween two points, it is still not guaranteed that there won’t be long traveling timebetween the locations of two consecutive tasks. We need optimal assignments betweentasks and workers.In the scientific literature Generalized Assignment Problem (GAP) is a wellknownproblem which deals with the assignment of m workers to n tasks consideringseveral constraints. The primary purpose of my thesis project was to choose a heuristics(genetic algorithm, tabu search or ant colony optimization) to be implemented into SAPExtended Warehouse Management (SAP EWM) by with task assignment will be moreeffective between tasks and resources.After system analysis I had to realize that due different constraints and businessdemands only 1:1 assingments are allowed in SAP EWM. Because of that I had to use adifferent and simpler approach – instead of the introduced heuristics – which could gainbetter assignments during the test phase in several cases. In the thesis I described indetails what ware the most important questions and problems which emerged during theplanning of my optimized assignment method.

La technique de paramétrisation est très prometteuse pour la conception radio logicielle. La radio logicielle consiste à concevoir des systèmes multi-standards qui tirent bénéfice des possibilités de programmation ou de reconfiguration offertes par les composants de traitement la constituant. Cette thèse étudie la technique de paramétrisation par opérateurs communs. Les opérateurs communs sont des unités de traitements communes à plusieurs opérations qu'effectue un équipement, quelle que soit la couche du modèle OSI à laquelle elles appartiennent. La méthode proposée repose sur une approche théorique afin de résoudre le problème de conception d'un équipement multi-standards. Elle consiste en une optimisation d'un hypergraphe. La conception de l'équipement est représentée par des opérateurs à différents niveaux de granularité dans un graphe acyclique orienté. Le niveau le plus élevé représente une approche de conception d'équipements multi-standards de type Velcro. Plus les opérateurs sont bas dans le graphe, plus leur coût est faible en termes de complexité, mais plus il faut faire appel de fois à eux pour effectuer des opérations de différentes sortes. Nous décrivons ensuite en tant qu'exemples des conception basées sur les opérateurs DMFFT (dual mode FFT), LFSR (linear feedback shift register) et le cas du FRMFB (frequency response masking filter bank). Les solutions basées sur les opérateurs communs proposées dans cette thèse peuvent contribuer à optimiser la conception des futurs équipements multi-standards de radio logicielle qui devront supporter de nombreux standards de communication sans fil.

Most times people are unprepared to face natural disasters resulting in chaos, increased number of deaths, etc.Emergency responders need an efficiently working communication network to get in touch with the emergency services like hospitals, police, fire and rescue as well as people who are stranded. Such a network is also the need of the hour for survivors to contact their near and dear ones. One of the major barriers of communication during an emergency is the destruction of network elements. In case the communication devices survive the calamity, odds of the network getting congested are certainly high because almost everyone will be trying to use the same network resources. An important factor when dealing with emergency situations is the calls for an immediate response and an efficient Emergency Communication Systems (ECS). Currently there is a capability gap between existing ECS solutions and what we dream of achieving. Most current solutions do not meet cost or mobility constraints. An inexpensive, portable and mobile system will fulfill this capability gap. The main purpose of this research is to optimize the altitude and received signal strength of an aerial base station to provide maximum radio coverage on the ground as well as propose the best fit radio propagation channel model to carry out the experiment for the current scenario.