@phdthesis{Lechner2022, author = {Lechner, Theresa}, title = {Proximal Methods for Nonconvex Composite Optimization Problems}, doi = {10.25972/OPUS-28907}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-289073}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2022}, abstract = {Optimization problems with composite functions deal with the minimization of the sum of a smooth function and a convex nonsmooth function. In this thesis several numerical methods for solving such problems in finite-dimensional spaces are discussed, which are based on proximity operators. After some basic results from convex and nonsmooth analysis are summarized, a first-order method, the proximal gradient method, is presented and its convergence properties are discussed in detail. Known results from the literature are summarized and supplemented by additional ones. Subsequently, the main part of the thesis is the derivation of two methods which, in addition, make use of second-order information and are based on proximal Newton and proximal quasi-Newton methods, respectively. The difference between the two methods is that the first one uses a classical line search, while the second one uses a regularization parameter instead. Both techniques lead to the advantage that, in contrast to many similar methods, in the respective detailed convergence analysis global convergence to stationary points can be proved without any restricting precondition. Furthermore, comprehensive results show the local convergence properties as well as convergence rates of these algorithms, which are based on rather weak assumptions. Also a method for the solution of the arising proximal subproblems is investigated. In addition, the thesis contains an extensive collection of application examples and a detailed discussion of the related numerical results.}, subject = {Optimierung}, language = {en} } @phdthesis{Herrmann2021, author = {Herrmann, Marc}, title = {The Total Variation on Surfaces and of Surfaces}, doi = {10.25972/OPUS-24073}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-240736}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2021}, abstract = {This thesis is concerned with applying the total variation (TV) regularizer to surfaces and different types of shape optimization problems. The resulting problems are challenging since they suffer from the non-differentiability of the TV-seminorm, but unlike most other priors it favors piecewise constant solutions, which results in piecewise flat geometries for shape optimization problems.The first part of this thesis deals with an analogue of the TV image reconstruction approach [Rudin, Osher, Fatemi (Physica D, 1992)] for images on smooth surfaces. A rigorous analytical framework is developed for this model and its Fenchel predual, which is a quadratic optimization problem with pointwise inequality constraints on the surface. A function space interior point method is proposed to solve it. Afterwards, a discrete variant (DTV) based on a nodal quadrature formula is defined for piecewise polynomial, globally discontinuous and continuous finite element functions on triangulated surface meshes. DTV has favorable properties, which include a convenient dual representation. Next, an analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. Its analysis is based on a differential geometric setting in which the unit normal vector is viewed as an element of the two-dimensional sphere manifold. Shape calculus is used to characterize the relevant derivatives and an variant of the split Bregman method for manifold valued functions is proposed. This is followed by an extension of the total variation prior for the normal vector field for piecewise flat surfaces and the previous variant of split Bregman method is adapted. Numerical experiments confirm that the new prior favours polyhedral shapes.}, subject = {Gestaltoptimierung}, language = {en} } @phdthesis{Karl2020, author = {Karl, Veronika}, title = {Augmented Lagrangian Methods for State Constrained Optimal Control Problems}, doi = {10.25972/OPUS-21384}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-213846}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2020}, abstract = {This thesis is concerned with the solution of control and state constrained optimal control problems, which are governed by elliptic partial differential equations. Problems of this type are challenging since they suffer from the low regularity of the multiplier corresponding to the state constraint. Applying an augmented Lagrangian method we overcome these difficulties by working with multiplier approximations in \$L^2(\Omega)\$. For each problem class, we introduce the solution algorithm, carry out a thoroughly convergence analysis and illustrate our theoretical findings with numerical examples. The thesis is divided into two parts. The first part focuses on classical PDE constrained optimal control problems. We start by studying linear-quadratic objective functionals, which include the standard tracking type term and an additional regularization term as well as the case, where the regularization term is replaced by an \$L^1(\Omega)\$-norm term, which makes the problem ill-posed. We deepen our study of the augmented Lagrangian algorithm by examining the more complicated class of optimal control problems that are governed by a semilinear partial differential equation. The second part investigates the broader class of multi-player control problems. While the examination of jointly convex generalized Nash equilibrium problems (GNEP) is a simple extension of the linear elliptic optimal control case, the complexity is increased significantly for pure GNEPs. The existence of solutions of jointly convex GNEPs is well-studied. However, solution algorithms may suffer from non-uniqueness of solutions. Therefore, the last part of this thesis is devoted to the analysis of the uniqueness of normalized equilibria.}, subject = {Optimale Kontrolle}, language = {en} } @phdthesis{Boergens2020, author = {B{\"o}rgens, Eike Alexander Lars Guido}, title = {ADMM-Type Methods for Optimization and Generalized Nash Equilibrium Problems in Hilbert Spaces}, doi = {10.25972/OPUS-21877}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-218777}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2020}, abstract = {This thesis is concerned with a certain class of algorithms for the solution of constrained optimization problems and generalized Nash equilibrium problems in Hilbert spaces. This class of algorithms is inspired by the alternating direction method of multipliers (ADMM) and eliminates the constraints using an augmented Lagrangian approach. The alternating direction method consists of splitting the augmented Lagrangian subproblem into smaller and more easily manageable parts. Before the algorithms are discussed, a substantial amount of background material, including the theory of Banach and Hilbert spaces, fixed-point iterations as well as convex and monotone set-valued analysis, is presented. Thereafter, certain optimization problems and generalized Nash equilibrium problems are reformulated and analyzed using variational inequalities and set-valued mappings. The analysis of the algorithms developed in the course of this thesis is rooted in these reformulations as variational inequalities and set-valued mappings. The first algorithms discussed and analyzed are one weakly and one strongly convergent ADMM-type algorithm for convex, linearly constrained optimization. By equipping the associated Hilbert space with the correct weighted scalar product, the analysis of these two methods is accomplished using the proximal point method and the Halpern method. The rest of the thesis is concerned with the development and analysis of ADMM-type algorithms for generalized Nash equilibrium problems that jointly share a linear equality constraint. The first class of these algorithms is completely parallelizable and uses a forward-backward idea for the analysis, whereas the second class of algorithms can be interpreted as a direct extension of the classical ADMM-method to generalized Nash equilibrium problems. At the end of this thesis, the numerical behavior of the discussed algorithms is demonstrated on a collection of examples.}, subject = {Constrained optimization}, language = {en} } @phdthesis{Lange2019, author = {Lange, Stanislav}, title = {Optimization of Controller Placement and Information Flow in Softwarized Networks}, issn = {1432-8801}, doi = {10.25972/OPUS-17457}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-174570}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2019}, abstract = {The Software Defined Networking (SDN) paradigm offers network operators numerous improvements in terms of flexibility, scalability, as well as cost efficiency and vendor independence. However, in order to maximize the benefit from these features, several new challenges in areas such as management and orchestration need to be addressed. This dissertation makes contributions towards three key topics from these areas. Firstly, we design, implement, and evaluate two multi-objective heuristics for the SDN controller placement problem. Secondly, we develop and apply mechanisms for automated decision making based on the Pareto frontiers that are returned by the multi-objective optimizers. Finally, we investigate and quantify the performance benefits for the SDN control plane that can be achieved by integrating information from external entities such as Network Management Systems (NMSs) into the control loop. Our evaluation results demonstrate the impact of optimizing various parameters of softwarized networks at different levels and are used to derive guidelines for an efficient operation.}, subject = {Leistungsbewertung}, language = {en} } @phdthesis{Peng2019, author = {Peng, Dongliang}, title = {An Optimization-Based Approach for Continuous Map Generalization}, edition = {1. Auflage}, publisher = {W{\"u}rzburg University Press}, address = {W{\"u}rzburg}, isbn = {978-3-95826-104-4}, doi = {10.25972/WUP-978-3-95826-105-1}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-174427}, school = {W{\"u}rzburg University Press}, pages = {xv, 132}, year = {2019}, abstract = {Maps are the main tool to represent geographical information. Geographical information is usually scale-dependent, so users need to have access to maps at different scales. In our digital age, the access is realized by zooming. As discrete changes during the zooming tend to distract users, smooth changes are preferred. This is why some digital maps are trying to make the zooming as continuous as they can. The process of producing maps at different scales with smooth changes is called continuous map generalization. In order to produce maps of high quality, cartographers often take into account additional requirements. These requirements are transferred to models in map generalization. Optimization for map generalization is important not only because it finds optimal solutions in the sense of the models, but also because it helps us to evaluate the quality of the models. Optimization, however, becomes more delicate when we deal with continuous map generalization. In this area, there are requirements not only for a specific map but also for relations between maps at difference scales. This thesis is about continuous map generalization based on optimization. First, we show the background of our research topics. Second, we find optimal sequences for aggregating land-cover areas. We compare the A\$^{\!\star}\$\xspace algorithm and integer linear programming in completing this task. Third, we continuously generalize county boundaries to provincial boundaries based on compatible triangulations. We morph between the two sets of boundaries, using dynamic programming to compute the correspondence. Fourth, we continuously generalize buildings to built-up areas by aggregating and growing. In this work, we group buildings with the help of a minimum spanning tree. Fifth, we define vertex trajectories that allow us to morph between polylines. We require that both the angles and the edge lengths change linearly over time. As it is impossible to fulfill all of these requirements simultaneously, we mediate between them using least-squares adjustment. Sixth, we discuss the performance of some commonly used data structures for a specific spatial problem. Seventh, we conclude this thesis and present open problems.}, subject = {Generalisierung }, language = {en} } @phdthesis{Steck2018, author = {Steck, Daniel}, title = {Lagrange Multiplier Methods for Constrained Optimization and Variational Problems in Banach Spaces}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-174444}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2018}, abstract = {This thesis is concerned with a class of general-purpose algorithms for constrained minimization problems, variational inequalities, and quasi-variational inequalities in Banach spaces. A substantial amount of background material from Banach space theory, convex analysis, variational analysis, and optimization theory is presented, including some results which are refinements of those existing in the literature. This basis is used to formulate an augmented Lagrangian algorithm with multiplier safeguarding for the solution of constrained optimization problems in Banach spaces. The method is analyzed in terms of local and global convergence, and many popular problem classes such as nonlinear programming, semidefinite programming, and function space optimization are shown to be included as special cases of the general setting. The algorithmic framework is then extended to variational and quasi-variational inequalities, which include, by extension, Nash and generalized Nash equilibrium problems. For these problem classes, the convergence is analyzed in detail. The thesis then presents a rich collection of application examples for all problem classes, including implementation details and numerical results.}, subject = {Optimierung}, language = {en} } @phdthesis{Sprengel2017, author = {Sprengel, Martin}, title = {A Theoretical and Numerical Analysis of a Kohn-Sham Equation and Related Control Problems}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-153545}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2017}, abstract = {In this work, multi-particle quantum optimal control problems are studied in the framework of time-dependent density functional theory (TDDFT). Quantum control problems are of great importance in both fundamental research and application of atomic and molecular systems. Typical applications are laser induced chemical reactions, nuclear magnetic resonance experiments, and quantum computing. Theoretically, the problem of how to describe a non-relativistic system of multiple particles is solved by the Schr{\"o}dinger equation (SE). However, due to the exponential increase in numerical complexity with the number of particles, it is impossible to directly solve the Schr{\"o}dinger equation for large systems of interest. An efficient and successful approach to overcome this difficulty is the framework of TDDFT and the use of the time-dependent Kohn-Sham (TDKS) equations therein. This is done by replacing the multi-particle SE with a set of nonlinear single-particle Schr{\"o}dinger equations that are coupled through an additional potential. Despite the fact that TDDFT is widely used for physical and quantum chemical calculation and software packages for its use are readily available, its mathematical foundation is still under active development and even fundamental issues remain unproven today. The main purpose of this thesis is to provide a consistent and rigorous setting for the TDKS equations and of the related optimal control problems. In the first part of the thesis, the framework of density functional theory (DFT) and TDDFT are introduced. This includes a detailed presentation of the different functional sets forming DFT. Furthermore, the known equivalence of the TDKS system to the original SE problem is further discussed. To implement the TDDFT framework for multi-particle computations, the TDKS equations provide one of the most successful approaches nowadays. However, only few mathematical results concerning these equations are available and these results do not cover all issues that arise in the formulation of optimal control problems governed by the TDKS model. It is the purpose of the second part of this thesis to address these issues such as higher regularity of TDKS solutions and the case of weaker requirements on external (control) potentials that are instrumental for the formulation of well-posed TDKS control problems. For this purpose, in this work, existence and uniqueness of TDKS solutions are investigated in the Galerkin framework and using energy estimates for the nonlinear TDKS equations. In the third part of this thesis, optimal control problems governed by the TDKS model are formulated and investigated. For this purpose, relevant cost functionals that model the purpose of the control are discussed. Henceforth, TDKS control problems result from the requirement of optimising the given cost functionals subject to the differential constraint given by the TDKS equations. The analysis of these problems is novel and represents one of the main contributions of the present thesis. In particular, existence of minimizers is proved and their characterization by TDKS optimality systems is discussed in detail. To this end, Fr{\´e}chet differentiability of the TDKS model and of the cost functionals is addressed considering \(H^1\) cost of the control. This part is concluded by deriving the reduced gradient in the \(L^2\) and \(H^1\) inner product. While the \(L^2\) optimization is widespread in the literature, the choice of the \(H^1\) gradient is motivated in this work by theoretical consideration and by resulting numerical advantages. The last part of the thesis is devoted to the numerical approximation of the TDKS optimality systems and to their solution by gradient-based optimization techniques. For the former purpose, Strang time-splitting pseudo-spectral schemes are discussed including a review of some recent theoretical estimates for these schemes and a numerical validation of these estimates. For the latter purpose, nonlinear (projected) conjugate gradient methods are implemented and are used to validate the theoretical analysis of this thesis with results of numerical experiments with different cost functional settings.}, subject = {Optimale Kontrolle}, language = {en} } @phdthesis{Schwartz2016, author = {Schwartz, Christian}, title = {Modeling and Evaluation of Multi-Stakeholder Scenarios in Communication Networks}, issn = {1432-8801}, doi = {10.25972/OPUS-13388}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-133887}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2016}, abstract = {Today's Internet is no longer only controlled by a single stakeholder, e.g. a standard body or a telecommunications company. Rather, the interests of a multitude of stakeholders, e.g. application developers, hardware vendors, cloud operators, and network operators, collide during the development and operation of applications in the Internet. Each of these stakeholders considers different KPIs to be important and attempts to optimise scenarios in its favour. This results in different, often opposing views and can cause problems for the complete network ecosystem. One example of such a scenario are Signalling Storms in the mobile Internet, with one of the largest occurring in Japan in 2012 due to the release and high popularity of a free instant messaging application. The network traffic generated by the application caused a high number of connections to the Internet being established and terminated. This resulted in a similarly high number of signalling messages in the mobile network, causing overload and a loss of service for 2.5 million users over 4 hours. While the network operator suffers the largest impact of this signalling overload, it does not control the application. Thus, the network operator can not change the application traffic characteristics to generate less network signalling traffic. The stakeholders who could prevent, or at least reduce, such behaviour, i.e. application developers or hardware vendors, have no direct benefit from modifying their products in such a way. This results in a clash of interests which negatively impacts the network performance for all participants. The goal of this monograph is to provide an overview over the complex structures of stakeholder relationships in today's Internet applications in mobile networks. To this end, we study different scenarios where such interests clash and suggest methods where tradeoffs can be optimised for all participants. If such an optimisation is not possible or attempts at it might lead to adverse effects, we discuss the reasons.}, subject = {Leistungsbewertung}, language = {en} } @phdthesis{Hartmann2015, author = {Hartmann, Matthias}, title = {Optimization and Design of Network Architectures for Future Internet Routing}, issn = {1432-8801}, doi = {10.25972/OPUS-11416}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-114165}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2015}, abstract = {At the center of the Internet's protocol stack stands the Internet Protocol (IP) as a common denominator that enables all communication. To make routing efficient, resilient, and scalable, several aspects must be considered. Care must be taken that traffic is well balanced to make efficient use of the existing network resources, both in failure free operation and in failure scenarios. Finding the optimal routing in a network is an NP-complete problem. Therefore, routing optimization is usually performed using heuristics. This dissertation shows that a routing optimized with one objective function is often not good when looking at other objective functions. It can even be worse than unoptimized routing with respect to that objective function. After looking at failure-free routing and traffic distribution in different failure scenarios, the analysis is extended to include the loop-free alternate (LFA) IP fast reroute mechanism. Different application scenarios of LFAs are examined and a special focus is set on the fact that LFAs usually cannot protect all traffic in a network even against single link failures. Thus, the routing optimization for LFAs is targeted on both link utilization and failure coverage. Finally, the pre-congestion notification mechanism PCN for network admission control and overload protection is analyzed and optimized. Different design options for implementing the protocol are compared, before algorithms are developed for the calculation and optimization of protocol parameters and PCN-based routing. The second part of the thesis tackles a routing problem that can only be resolved on a global scale. The scalability of the Internet is at risk since a major and intensifying growth of the interdomain routing tables has been observed. Several protocols and architectures are analyzed that can be used to make interdomain routing more scalable. The most promising approach is the locator/identifier (Loc/ID) split architecture which separates routing from host identification. This way, changes in connectivity, mobility of end hosts, or traffic-engineering activities are hidden from the routing in the core of the Internet and the routing tables can be kept much smaller. All of the currently proposed Loc/ID split approaches have their downsides. In particular, the fact that most architectures use the ID for routing outside the Internet's core is a poor design, which inhibits many of the possible features of a new routing architecture. To better understand the problems and to provide a solution for a scalable routing design that implements a true Loc/ID split, the new GLI-Split protocol is developed in this thesis, which provides separation of global and local routing and uses an ID that is independent from any routing decisions. Besides GLI-Split, several other new routing architectures implementing Loc/ID split have been proposed for the Internet. Most of them assume that a mapping system is queried for EID-to-RLOC mappings by an intermediate node at the border of an edge network. When the mapping system is queried by an intermediate node, packets are already on their way towards their destination, and therefore, the mapping system must be fast, scalable, secure, resilient, and should be able to relay packets without locators to nodes that can forward them to the correct destination. The dissertation develops a classification for all proposed mapping system architectures and shows their similarities and differences. Finally, the fast two-level mapping system FIRMS is developed. It includes security and resilience features as well as a relay service for initial packets of a flow when intermediate nodes encounter a cache miss for the EID-to-RLOC mapping.}, subject = {Netzwerk}, language = {en} } @phdthesis{Hock2014, author = {Hock, David Rog{\´e}r}, title = {Analysis and Optimization of Resilient Routing in Core Communication Networks}, issn = {1432-8801}, doi = {10.25972/OPUS-10168}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-101681}, school = {Universit{\"a}t W{\"u}rzburg}, pages = {175}, year = {2014}, abstract = {Routing is one of the most important issues in any communication network. It defines on which path packets are transmitted from the source of a connection to the destination. It allows to control the distribution of flows between different locations in the network and thereby is a means to influence the load distribution or to reach certain constraints imposed by particular applications. As failures in communication networks appear regularly and cannot be completely avoided, routing is required to be resilient against such outages, i.e., routing still has to be able to forward packets on backup paths even if primary paths are not working any more. Throughout the years, various routing technologies have been introduced that are very different in their control structure, in their way of working, and in their ability to handle certain failure cases. Each of the different routing approaches opens up their own specific questions regarding configuration, optimization, and inclusion of resilience issues. This monograph investigates, with the example of three particular routing technologies, some concrete issues regarding the analysis and optimization of resilience. It thereby contributes to a better general, technology-independent understanding of these approaches and of their diverse potential for the use in future network architectures. The first considered routing type, is decentralized intra-domain routing based on administrative IP link costs and the shortest path principle. Typical examples are common today's intra-domain routing protocols OSPF and IS-IS. This type of routing includes automatic restoration abilities in case of failures what makes it in general very robust even in the case of severe network outages including several failed components. Furthermore, special IP-Fast Reroute mechanisms allow for a faster reaction on outages. For routing based on link costs, traffic engineering, e.g. the optimization of the maximum relative link load in the network, can be done indirectly by changing the administrative link costs to adequate values. The second considered routing type, MPLS-based routing, is based on the a priori configuration of primary and backup paths, so-called Label Switched Paths. The routing layout of MPLS paths offers more freedom compared to IP-based routing as it is not restricted by any shortest path constraints but any paths can be setup. However, this in general involves a higher configuration effort. Finally, in the third considered routing type, typically centralized routing using a Software Defined Networking (SDN) architecture, simple switches only forward packets according to routing decisions made by centralized controller units. SDN-based routing layouts offer the same freedom as for explicit paths configured using MPLS. In case of a failure, new rules can be setup by the controllers to continue the routing in the reduced topology. However, new resilience issues arise caused by the centralized architecture. If controllers are not reachable anymore, the forwarding rules in the single nodes cannot be adapted anymore. This might render a rerouting in case of connection problems in severe failure scenarios infeasible.}, subject = {Leistungsbewertung}, language = {en} } @phdthesis{Curtef2012, author = {Curtef, Oana}, title = {Rayleigh-quotient optimization on tensor products of Grassmannians}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-83383}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2012}, abstract = {Applications in various research areas such as signal processing, quantum computing, and computer vision, can be described as constrained optimization tasks on certain subsets of tensor products of vector spaces. In this work, we make use of techniques from Riemannian geometry and analyze optimization tasks on subsets of so-called simple tensors which can be equipped with a differentiable structure. In particular, we introduce a generalized Rayleigh-quotient function on the tensor product of Grassmannians and on the tensor product of Lagrange- Grassmannians. Its optimization enables a unified approach to well-known tasks from different areas of numerical linear algebra, such as: best low-rank approximations of tensors (data compression), computing geometric measures of entanglement (quantum computing) and subspace clustering (image processing). We perform a thorough analysis on the critical points of the generalized Rayleigh-quotient and develop intrinsic numerical methods for its optimization. Explicitly, using the techniques from Riemannian optimization, we present two type of algorithms: a Newton-like and a conjugated gradient algorithm. Their performance is analysed and compared with established methods from the literature.}, subject = {Optimierung}, language = {en} } @phdthesis{Ehses2011, author = {Ehses, Philipp}, title = {Development of new Acquisition Strategies for fast Parameter Quantification in Magnetic Resonance Imaging}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-72531}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2011}, abstract = {Magnetic resonance imaging (MRI) is a medical imaging method that involves no ionizing radiation and can be used non-invasively. Another important - if not the most important - reason for the widespread and increasing use of MRI in clinical practice is its interesting and highly flexible image contrast, especially of biological tissue. The main disadvantages of MRI, compared to other widespread imaging modalities like computed tomography (CT), are long measurement times and the directly resulting high costs. In the first part of this work, a new technique for accelerated MRI parameter mapping using a radial IR TrueFISP sequence is presented. IR TrueFISP is a very fast method for the simultaneous quantification of proton density, the longitudinal relaxation time T1, and the transverse relaxation time T2. Chapter 2 presents speed improvements to the original IR TrueFISP method. Using a radial view-sharing technique, it was possible to obtain a full set of relaxometry data in under 6 s per slice. Furthermore, chapter 3 presents the investigation and correction of two major sources of error of the IR TrueFISP method, namely magnetization transfer and imperfect slice profiles. In the second part of this work, a new MRI thermometry method is presented that can be used in MRI-safety investigations of medical implants, e.g. cardiac pacemakers and implantable cardioverter-defibrillators (ICDs). One of the major safety risks associated with MRI examinations of pacemaker and ICD patients is RF induced heating of the pacing electrodes. The design of MRI-safe (or MRI-conditional) pacing electrodes requires elaborate testing. In a first step, many different electrode shapes, electrode positions and sequence parameters are tested in a gel phantom with its geometry and conductivity matched to a human body. The resulting temperature increase is typically observed using temperature probes that are placed at various positions in the gel phantom. An alternative to this local thermometry approach is to use MRI for the temperature measurement. Chapter 5 describes a new approach for MRI thermometry that allows MRI thermometry during RF heating caused by the MRI sequence itself. Specifically, a proton resonance frequency (PRF) shift MRI thermometry method was combined with an MR heating sequence. The method was validated in a gel phantom, with a copper wire serving as a simple model for a medical implant.}, subject = {Kernspintomografie}, language = {en} } @phdthesis{Staehle2011, author = {Staehle, Barbara}, title = {Modeling and Optimization Methods for Wireless Sensor and Mesh Networks}, doi = {10.25972/OPUS-4967}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-64884}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2011}, abstract = {Im Internet der Zukunft werden Menschen nicht nur mit Menschen, sondern auch mit „Dingen", und sogar „Dinge" mit „Dingen" kommunizieren. Zus{\"a}tzlich wird das Bed{\"u}rfnis steigen, immer und {\"u}berall Zugang zum Internet zu haben. Folglich gewinnen drahtlose Sensornetze (WSNs) und drahtlose Mesh-Netze (WMNs) an Bedeutung, da sie Daten {\"u}ber die Umwelt ins Internet liefern, beziehungsweise einfache Internet-Zugangsm{\"o}glichkeiten schaffen. In den vier Teilen dieser Arbeit werden unterschiedliche Modellierungs- und Optimierungsmethoden f{\"u}r WSNs und WMNs vorgestellt. Der Energieverbrauch ist die wichtigste Metrik, wenn es darum geht die Kommunikation in einem WSN zu optimieren. Da sich in der Literatur sehr viele unterschiedliche Energiemodelle finden, untersucht der erste Teil der Arbeit welchen Einfluss unterschiedliche Energiemodelle auf die Optimierung von WSNs haben. Aufbauend auf diesen {\"U}berlegungen besch{\"a}ftigt sich der zweite Teil der Arbeit mit drei Problemen, die {\"u}berwunden werden m{\"u}ssen um eine standardisierte energieeffiziente Kommunikations-L{\"o}sung f{\"u}r WSNs basierend auf IEEE 802.15.4 und ZigBee zu realisieren. F{\"u}r WMNs sind beide Probleme von geringem Interesse, die Leistung des Netzes jedoch umso mehr. Der dritte Teil der Arbeit f{\"u}hrt daher Algorithmen f{\"u}r die Berechnung des Max-Min fairen (MMF) Netzwerk-Durchsatzes in WMNs mit mehreren Linkraten und Internet-Gateways ein. Der letzte Teil der Arbeit untersucht die Auswirkungen des LRA-Konzeptes. Dessen grundlegende Idee ist die folgende. Falls f{\"u}r einen Link eine niedrigere Datenrate als theoretisch m{\"o}glich verwendet wird, sinkt zwar der Link-Durchsatz, jedoch ist unter Umst{\"a}nden eine gr{\"o}ßere Anzahl von gleichzeitigen {\"U}bertragungen m{\"o}glich und der Gesamt-Durchsatz des Netzes kann sich erh{\"o}hen. Mithilfe einer analytischen LRA Formulierung und einer systematischen Studie kann gezeigt werden, dass eine netzwerkweite Zuordnung robusterer Datenraten als n{\"o}tig zu einer Erh{\"o}hung des MMF Netzwerk-Durchsatzes f{\"u}hrt. Desweitern kann gezeigt werden, dass sich LRA positiv auf die Leistungsf{\"a}higkeit eines IEEE 802.11 WMNs auswirkt und f{\"u}r die Optimierung des Netzes genutzt werden kann.}, subject = {Drahtloses Sensorsystem}, language = {en} } @phdthesis{Pries2010, author = {Pries, Jan Rastin}, title = {Performance Optimization of Wireless Infrastructure and Mesh Networks}, doi = {10.25972/OPUS-3723}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-46097}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2010}, abstract = {Future broadband wireless networks should be able to support not only best effort traffic but also real-time traffic with strict Quality of Service (QoS) constraints. In addition, their available resources are scare and limit the number of users. To facilitate QoS guarantees and increase the maximum number of concurrent users, wireless networks require careful planning and optimization. In this monograph, we studied three aspects of performance optimization in wireless networks: resource optimization in WLAN infrastructure networks, quality of experience control in wireless mesh networks, and planning and optimization of wireless mesh networks. An adaptive resource management system is required to effectively utilize the limited resources on the air interface and to guarantee QoS for real-time applications. Thereby, both WLAN infrastructure and WLAN mesh networks have to be considered. An a-priori setting of the access parameters is not meaningful due to the contention-based medium access and the high dynamics of the system. Thus, a management system is required which dynamically adjusts the channel access parameters based on the network load. While this is sufficient for wireless infrastructure networks, interferences on neighboring paths and self-interferences have to be considered for wireless mesh networks. In addition, a careful channel allocation and route assignment is needed. Due to the large parameter space, standard optimization techniques fail for optimizing large wireless mesh networks. In this monograph, we reveal that biology-inspired optimization techniques, namely genetic algorithms, are well-suitable for the planning and optimization of wireless mesh networks. Although genetic algorithms generally do not always find the optimal solution, we show that with a good parameter set for the genetic algorithm, the overall throughput of the wireless mesh network can be significantly improved while still sharing the resources fairly among the users.}, subject = {IEEE 802.11}, language = {en} } @phdthesis{Klug2006, author = {Klug, Andreas}, title = {Affine-Scaling Methods for Nonlinear Minimization Problems and Nonlinear Systems of Equations with Bound Constraints}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-18851}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2006}, abstract = {In this thesis affine-scaling-methods for two different types of mathematical problems are considered. The first type of problems are nonlinear optimization problems subject to bound constraints. A class of new affine-scaling Newton-type methods is introduced. The methods are shown to be locally quadratically convergent without assuming strict complementarity of the solution. The new methods differ from previous ones mainly in the choice of the scaling matrix. The second type of problems are semismooth system of equations with bound constraints. A new affine-scaling trust-region method for these problems is developed. The method is shown to have strong global and local convergence properties under suitable assumptions. Numerical results are presented for a number of problems arising from different areas.}, subject = {Skalierungsfunktion}, language = {en} }