This thesis presents a predictive energy management controller for long-haul hybrid trucks. In a receding horizon control framework, the vehicle speed reference, battery energy reference, and engine on/off decision are optimized over a prediction horizon. A mixed-integer quadratic program (MIQP) is formulated by performing modelling approximations and by including the binary engine on/off decision in the optimal control problem. The branch-and-bound algorithm is applied to solve this problem. Simulation results show fuel consumption reductions between 10-15%, depending on driving cycle, compared to a conventional truck. The hybrid truck without the predictive control saves significantly less. Fuel consumption is reduced by 3-8% in this case. A sensitivity analysis studies the effects on branch-and-bound iterations and fuel consumption when varying parameters related to the binary engine on/off decision. In addition, it is shown that the control strategy can maintain a safe time gap to a leading vehicle. Also, the introduction of the battery temperature state makes it possible to approximately model the dynamic battery power limitations over the prediction horizon. The main contributions of the thesis are the MIQP control problem formulation, the strategy to solve this with the branch-and-bound method, and the sensitivity analysis.

No description available.

The aim of this work is to make some investigations concerning duality for multiobjective optimization problems. In order to do this we study first the duality for scalar optimization problems by using the conjugacy approach. This allows us to attach three different dual problems to a primal one. We examine the relations between the optimal objective values of the duals and verify, under some appropriate assumptions, the existence of strong duality. Closely related to the strong duality we derive the optimality conditions for each of these three duals. By means of these considerations, we study the duality for two vector optimization problems, namely, a convex multiobjective problem with cone inequality constraints and a special fractional programming problem with linear inequality constraints. To each of these vector problems we associate a scalar primal and study the duality for it. The structure of both scalar duals give us an idea about how to construct a multiobjective dual. The existence of weak and strong duality is also shown. We conclude our investigations by making an analysis over different duality concepts in multiobjective optimization. To a general multiobjective problem with cone inequality constraints we introduce other six different duals for which we prove weak as well as strong duality assertions. Afterwards, we derive some inclusion results for the image sets and, respectively, for the maximal elements sets of the image sets of these problems. Moreover, we show under which conditions they become identical. A general scheme containing the relations between the six multiobjective duals and some other duals mentioned in the literature is derived. / Das Ziel dieser Arbeit ist die Durchführung einiger Untersuchungen bezüglich der Dualität für Mehrzieloptimierungsaufgaben. Zu diesem Zweck wird als erstes mit Hilfe des so genannten konjugierten Verfahrens die Dualität für skalare Optimierungsaufgaben untersucht. Das erlaubt uns zu einer primalen Aufgabe drei unterschiedliche duale Aufgaben zuzuordnen. Wir betrachten die Beziehungen zwischen den optimalen Zielfunktionswerten der drei Dualaufgaben und untersuchen die Existenz der starken Dualität unter naheliegenden Annahmen. Im Zusammenhang mit der starken Dualität leiten wir für jede dieser Dualaufgaben die Optimalitätsbedingungen her. Die obengenannten Ergebnisse werden beim Studium der Dualität für zwei Vektoroptimierungsaufgaben angewandt, und zwar für die konvexe Mehrzieloptimierungsaufgabe mit Kegel-Ungleichungen als Nebenbedingungen und für eine spezielle Quotientenoptimierungsaufgabe mit linearen Ungleichungen als Nebenbedingungen. Wir assoziieren zu jeder dieser vektoriellen Aufgaben eine skalare Aufgabe für welche die Dualität betrachtet wird. Die Formulierung der beiden skalaren Dualaufgaben führt uns zu der Konstruktion der Mehrzieloptimierungsaufgabe. Die Existenz von schwacher und starker Dualität wird bewiesen. Wir schliessen unsere Untersuchungen ab, indem wir eine Analyse von verschiedenen Dualitätskonzepten in der Mehrzieloptimierung durchführen. Zu einer allgemeinen Mehrzieloptimierungsaufgabe mit Kegel-Ungleichungen als Nebenbedingungen werden sechs verschiedene Dualaufgaben eingeführt, für die sowohl schwache als auch starke Dualitätsaussagen gezeigt werden. Danach leiten wir verschiedene Beziehungen zwischen den Bildmengen, bzw., zwischen den Mengen der maximalen Elemente dieser Bildmengen der sechs Dualaufgaben her. Dazu zeigen wir unter welchen Bedingungen werden diese Mengen identisch. Ein allgemeines Schema das die Beziehungen zwischen den sechs dualen Mehrzieloptimierungsaufgaben und andere Dualaufgaben aus der Literatur enthält, wird dargestellt.

As the title already suggests the aim of the present work is to present Farkas - type results for inequality systems involving convex and/or non - convex functions. To be able to give the desired results, we treat optimization problems which involve convex and composed convex functions or non - convex functions like DC functions or fractions. To be able to use the fruitful Fenchel - Lagrange duality approach, to the primal problem we attach an equivalent problem which is a convex optimization problem. After giving a dual problem to the problem we initially treat, we provide weak necessary conditions which secure strong duality, i.e., the case when the optimal objective value of the primal problem coincides with the optimal objective value of the dual problem and, moreover, the dual problem has an optimal solution. Further, two ideas are followed. Firstly, using the weak and strong duality between the primal problem and the dual problem, we are able to give necessary and sufficient optimality conditions for the optimal solutions of the primal problem. Secondly, provided that no duality gap lies between the primal problem and its Fenchel - Lagrange - type dual we are able to demonstrate some Farkas - type results and thus to underline once more the connections between the theorems of the alternative and the theory of duality. One statement of the above mentioned Farkas - type results is characterized using only epigraphs of functions. We conclude our investigations by providing necessary and sufficient optimality conditions for a multiobjective programming problem involving composed convex functions. Using the well-known linear scalarization to the primal multiobjective program a family of scalar optimization problems is attached. Further to each of these scalar problems the Fenchel - Lagrange dual problem is determined. Making use of the weak and strong duality between the scalarized problem and its dual the desired optimality conditions are proved. Moreover, the way the dual problem of the scalarized problem looks like gives us an idea about how to construct a vector dual problem to the initial one. Further weak and strong vector duality assertions are provided.

<p>Online decision making with switching costs has received considerable attention in many practical problems that face uncertainty in the inputs and key problem parameters. Because of the switching costs that penalize the change of decisions, making good online decisions under such uncertainty is known to be extremely challenging. This thesis aims at providing new online algorithms with strong performance guarantees to address this challenge.</p> <p><br></p> <p>In part 1 and part 2 of this thesis, motivated by Network Functions Virtualization and smart grid, we study competitive online convex optimization with switching costs. Specifically, in part 1, we focus on the setting with an uncertainty set (one type of prediction) and hard infeasibility constraints. We develop new online algorithms that can attain optimized competitive ratios, while ensuring feasibility at all times. Moreover, we design a robustification procedure that helps these algorithms obtain good average-case performance simultaneously. In part 2, we focus on the setting with look-ahead (another type of prediction). We provide the first algorithm that attains a competitive ratio that not only decreases to 1 as the look-ahead window size increases, but also remains upper-bounded for any ratio between the switching-cost coefficient and service-cost coefficient.</p> <p><br></p> <p>In part 3 of this thesis, motivated by edge computing with artificial intelligence, we study bandit learning with switching costs where, in addition to bandit feedback, full feedback can be requested at a cost. We show that, when only 1 arm can be chosen at a time, adding costly full-feedback is not helpful in fundamentally reducing the Θ(<em>T</em>2/3) regret over a time-horizon <em>T</em>. In contrast, when 2 (or more) arms can be chosen at a time, we provide a new online learning algorithm that achieves a significantly smaller regret equal to <em>O</em>(√<em>T</em>), without even using full feedback. To the best of our knowledge, this type of sharp transition from choosing 1 arm to choosing 2 (or more) arms has never been reported in the literature.</p>

<p>Recent decades have witnessed the rise of data deluge generated by heterogeneous sources, e.g., social networks, streaming, marketing services etc., which has naturally created a surge of interests in theory and applications of large-scale convex and non-convex optimization. For example, real-world instances of statistical learning problems such as deep learning, recommendation systems, etc. can generate sheer volumes of spatially/temporally diverse data (up to Petabytes of data in commercial applications) with millions of decision variables to be optimized. Such problems are often referred to as Big-data problems. Solving these problems by standard optimization methods demands intractable amount of centralized storage and computational resources which is infeasible and is the foremost purpose of parallel and decentralized algorithms developed in this thesis.</p><p><br></p><p>This thesis consists of two parts: (I) Distributed Nonconvex Optimization and (II) Distributed Convex Optimization.</p><p><br></p><p>In Part (I), we start by studying a winning paradigm in big-data optimization, Block Coordinate Descent (BCD) algorithm, which cease to be effective when problem dimensions grow overwhelmingly. In particular, we considered a general family of constrained non-convex composite large-scale problems defined on multicore computing machines equipped with shared memory. We design a hybrid deterministic/random parallel algorithm to efficiently solve such problems combining synergically Successive Convex Approximation (SCA) with greedy/random dimensionality reduction techniques. We provide theoretical and empirical results showing efficacy of the proposed scheme in face of huge-scale problems. The next step is to broaden the network setting to general mesh networks modeled as directed graphs, and propose a class of gradient-tracking based algorithms with global convergence guarantees to critical points of the problem. We further explore the geometry of the landscape of the non-convex problems to establish second-order guarantees and strengthen our convergence to local optimal solutions results to global optimal solutions for a wide range of Machine Learning problems.</p><p><br></p><p>In Part (II), we focus on a family of distributed convex optimization problems defined over meshed networks. Relevant state-of-the-art algorithms often consider limited problem settings with pessimistic communication complexities with respect to the complexity of their centralized variants, which raises an important question: can one achieve the rate of centralized first-order methods over networks, and moreover, can one improve upon their communication costs by using higher-order local solvers? To answer these questions, we proposed an algorithm that utilizes surrogate objective functions in local solvers (hence going beyond first-order realms, such as proximal-gradient) coupled with a perturbed (push-sum) consensus mechanism that aims to track locally the gradient of the central objective function. The algorithm is proved to match the convergence rate of its centralized counterparts, up to multiplying network factors. When considering in particular, Empirical Risk Minimization (ERM) problems with statistically homogeneous data across the agents, our algorithm employing high-order surrogates provably achieves faster rates than what is achievable by first-order methods. Such improvements are made without exchanging any Hessian matrices over the network. </p><p><br></p><p>Finally, we focus on the ill-conditioning issue impacting the efficiency of decentralized first-order methods over networks which rendered them impractical both in terms of computation and communication cost. A natural solution is to develop distributed second-order methods, but their requisite for Hessian information incurs substantial communication overheads on the network. To work around such exorbitant communication costs, we propose a “statistically informed” preconditioned cubic regularized Newton method which provably improves upon the rates of first-order methods. The proposed scheme does not require communication of Hessian information in the network, and yet, achieves the iteration complexity of centralized second-order methods up to the statistical precision. In addition, (second-order) approximate nature of the utilized surrogate functions, improves upon the per-iteration computational cost of our earlier proposed scheme in this setting.</p>

Le problème de l'adaptation d'impédance en ingénierie des hyper fréquences et en électronique en général consiste à minimiser la réflexion de la puissance qui doit être transmise, par un générateur, à une charge donnée dans une bande de fréquence. Les exigences d'adaptation et de filtrage dans les systèmes de communication classiques sont généralement satisfaites en utilisant un circuit d'adaptation suivi d'un filtre. Nous proposons ici de concevoir des filtres d'adaptation qui intègrent à la fois les exigences d'adaptation et de filtrage dans un seul appareil et augmentent ainsi l'efficacité globale et la compacité du système. Dans ce travail, le problème d'adaptation est formulé en introduisant un problème d'optimisation convexe dans le cadre établi par la théorie de d'adaptation de Fano et Youla. De ce contexte, au moyen de techniques modernes de programmation semi-définies non linéaires, un problème convexe, et donc avec une optimalité garantie, est obtenu. Enfin, pour démontrer les avantages fournis par la théorie développée au-delà de la synthèse de filtres avec des charges complexes variables en fréquence, nous examinons deux applications pratiques récurrentes dans la conception de ce type de dispositifs. Ces applications correspondent, d'une part, à l'adaptation d'un réseau d'antennes dans le but de maximiser l'efficacité du rayonnement, et, d'autre part, à la synthèse de multiplexeurs où chacun des filtres de canal est adapté au reste du dispositif, notamment les filtres correspondant aux autres canaux. / The problem of impedance matching in electronics and particularly in RF engineering consists on minimising the reflection of the power that is to be transmitted, by a generator, to a given load within a frequency band. The matching and filtering requirements in classical communication systems are usually satisfied by using a matching circuit followed by a filter. We propose here to design matching filters that integrate both, matching and filtering requirements, in a single device and thereby increase the overall efficiency and compactness of the system. In this work, the matching problem is formulated by introducing convex optimisation on the framework established by the matching theory of Fano and Youla. As a result, by means of modern non-linear semi-definite programming techniques, a convex problem, and therefore with guaranteed optimality, is achieved. Finally, to demonstrate the advantages provided by the developed theory beyond the synthesis of filters with frequency varying loads, we consider two practical applications which are recurrent in the design of communication devices. These applications are, on the one hand, the matching of an array of antennas with the objective of maximizing the radiation efficiency, and on the other hand the synthesis of multiplexers where each of the channel filters is matched to the rest of the device, including the filters corresponding to the other channels.

Lagrangian relaxation is a successful solution approach for many combinatorial optimisation problems, one of them being the train timetabling problem (TTP). We model this problem using time expanded networks for the single train schedules and coupling constraints to enforce restrictions like station capacities and headway times. Lagrangian relaxation of these coupling constraints leads to shortest path subproblems in the time expanded networks and is solved using a proximal bundle method. However, large instances of our practical partner Deutsche Bahn lead to computationally intractable models. In this thesis we develop two new algorithmic techniques to improve the solution process for this kind of optimisation problems. The first new technique, Dynamic Graph Generation (DGG), aims at improving the computation of the shortest path subproblems in large time expanded networks. Without sacrificing any accuracy, DGG allows to store only small parts of the networks and to dynamically extend them whenever the stored part proves to be too small. This is possible by exploiting the properties of the objective function in many scheduling applications to prefer early paths or due times, respectively. We prove that DGG can be implemented very efficiently and its running time and the size of nodes that have to be stored additionally does not depend on the size of the time expanded network but only on the length of the train routes. The second technique is an asynchronous and parallel bundle method (APBM). Traditional bundle methods require one solution of each subproblem in each iteration. However, many practical applications, e.g. the TTP, consist of rather loosely coupled subproblems. The APBM chooses only small subspaces corresponding to the Lagrange multipliers of strongly violated coupling constraints and optimises only these variables while keeping all other variables fixed. Several subspaces of disjoint variables may be chosen simultaneously and are optimised in parallel. The solutions of the subspace problem are incorporated into the global data as soon as it is available without any synchronisation mechanism. However, in order to guarantee convergence, the algorithm detects automatically dependencies between different subspaces and respects these dependencies in future subspace selections. We prove the convergence of the APBM under reasonable assumptions for both, the dual and associated primal aggregate data. The APBM is then further extended to problems with unknown dependencies between subproblems and constraints in the Lagrangian relaxation problem. The algorithm automatically detects these dependencies and respects them in future iterations. Again we prove the convergence of this algorithm under reasonable assumptions. Finally we test our solution approach for the TTP on some real world instances of Deutsche Bahn. Using an iterative rounding heuristic based on the approximate fractional solutions obtained by the Lagrangian relaxation we are able to compute feasible schedules for all trains in a subnetwork of about 10% of the whole German network in about 12 hours. In these timetables 99% of all passenger trains could be scheduled with no significant delay and the travel time of the freight trains could be reduced by about one hour on average.

<p>The thesis intends to explain in full detail the developed techniques and approaches for the modeling, design, and sensitivity analysis of nano-plasmoic structures. However, some examples are included for audiences of general microwave background. Although the thesis is mainly focused on simulation-based techniques, analytical and convex optimization approaches are also demonstrated. The thesis is organized into two parts. Part 1 includes Chapters 2-4, which cover the simulation-based modeling and sensitivity analysis approaches and their applications. Part 2 includes Chapters 5 and 6, which cover the analytical optimization approaches.</p> / <p>We propose novel techniques for modeling, adjoint sensitivity analysis, and optimization of photonic and nano-plasmonic devices. The scope of our work is generalized to cover microwave, terahertz and optical regimes. It contains original approaches developed for different categories of materials including dispersive and plasmonic materials. Artificial materials (metamaterials) are also investigated and modeled. The modeling technique exploits the time-domain transmission line modeling (TD-TLM) technique. Generalized adjoint variable method (AVM) techniques are developed for sensitivity analysis of the modeled devices. Although TLM-based, they can be generalized to other time-domain modeling techniques like finite difference time-domain method (FDTD) and time-domain finite element method (FEM).</p> <p>We propose to extend the application of TLM-based AVM to photonic devices. We develop memory efficient approaches that overcome the limitation of excessive memory requirement in TLM-based AVM. A memory reduction of 90% can be achieved without loss of accuracy and at a more efficient calculation procedure. The developed technique is applied to slot waveguide Bragg gratings and a challenging dielectric resonator antenna problem.</p> <p>We also introduce a novel sensitivity analysis approach for materials with dispersive constitutive parameters. To our knowledge, this is the first wide-band AVM approach that takes into consideration the dependence of material properties on the frequency. The approach can be utilized for design optimization of innovative nano-plasmonic structures. The design of engineered metamaterial is systematic and efficient. Beside working with engineered new designs, dispersive AVM can be utilized in bio-imaging applications. The sensitivity of the objective function with respect to dispersive material properties enables the exploitation of parameter and gradient based optimization for imaging in the terahertz and optical regimes. Material resonance interaction can be easily investigated by the provided sensitivity information.</p> <p>In addition to the developed techniques for simulation-based optimization, several analytical optimization algorithms are proposed to foster the parameter extraction and design optimization in terahertz and optical regimes. In terahertz time-domain spectroscopy, we have developed an efficient parameter based approach that utilizes the pre-known information about the material. The algorithm allows for the estimation of the optical properties of sample materials of unknown thicknesses. The approach has been developed based on physical analytical dispersive models. It has been applied with the Debye, Lorentz, Cole-Cole, and Drude model.</p> <p>Furthermore, we propose various algorithms for design optimization of coupled resonators. The proposed algorithms are utilized to transform a highly non-linear optimization problem into a linear one. They exploit an approximate transfer function of the coupled resonators that avoids negligible multiple reflections among them. The algorithms are successful for the optimization of very large-scale coupled microcavities (150 coupled ring resonators).</p> / Doctor of Philosophy (PhD)

This research formulates and implements a novel closed-loop optimal control system that drives a train between two stations in an optimal time, energy efficient, or mixed objective manner. The optimal controller uses sensor feedback from the train and in real-time computes the most efficient control decision for the train to follow given knowledge of the track profile ahead of the train, speed restrictions and required arrival time windows. The control problem is solved both on an open track and while safely driving no closer than a fixed distance behind another locomotive. In contrast to other research in the field, this thesis achieves a real-time capable and embeddable closed-loop optimization with advanced modeling and numerical solving techniques with a non-linear optimal control problem. This controller is first formulated as a non-convex control problem and then converted to an advanced convex second-order cone problem with the intent of using a simple numerical solver, ensuring global optimality, and improving control robustness. Convex and non-convex numerical methods of solving the control problem are investigated and closed-loop performance results with a simulated vehicle are presented under realistic modeling conditions on advanced tracks both on desktop and embedded computer architectures. It is observed that the controller is capable of robust vehicle driving in cases both with and without modeling uncertainty. The benefits of pairing the optimal controller with a parameter estimator are demonstrated for cases where very large mismatches exists between the controller model and the simulated vehicle. Stopping performance is consistently within 25cm of target stations, and the worst case closed-loop optimization time was within 100ms for the computation of a 1000 point control horizon on an i7-6700 machine. / Thesis / Master of Applied Science (MASc) / This research formulates and implements a novel closed-loop optimal control system that drives a train between two stations in an optimal time, energy efficient, or mixed objective manner. It is deployed on a commuter vehicle and directly manages the motoring and braking systems. The optimal controller uses sensor feedback from the train and in real-time computes the most efficient control decision for the train to follow given knowledge of the track profile ahead of the train, speed restrictions and required arrival time windows. The final control implementation is capable of safe, high accuracy and optimal driving all while computing fast enough to reliably deploy on a rail vehicle.