- Table View
- List View
Optimal Social Influence (SpringerBriefs in Optimization)
by Weili Wu Wen XuThis self-contained book describes social influence from a computational point of view, with a focus on recent and practical applications, models, algorithms and open topics for future research. Researchers, scholars, postgraduates and developers interested in research on social networking and the social influence related issues will find this book useful and motivating. The latest research on social computing is presented along with and illustrations on how to understand and manipulate social influence for knowledge discovery by applying various data mining techniques in real world scenarios. Experimental reports, survey papers, models and algorithms with specific optimization problems are depicted. The main topics covered in this book are: chrematistics of social networks, modeling of social influence propagation, popular research problems in social influence analysis such as influence maximization, rumor blocking, rumor source detection, and multiple social influence competing.
Optimal Statistical Inference in Financial Engineering
by Masanobu Taniguchi Junichi Hirukawa Kenichiro TamakiUntil now, few systematic studies of optimal statistical inference for stochastic processes had existed in the financial engineering literature, even though this idea is fundamental to the field. Balancing statistical theory with data analysis, Optimal Statistical Inference in Financial Engineering examines how stochastic models can effectively des
Optimal Stochastic Control Schemes within a Structural Reliability Framework
by Bernt J. LeiraThe book addresses the topic of on-line implementation of structural and mechanical design criteria as an explicit part of optimal control schemes. The intention of the present research monograph is to reflect recent developments within this area. Examples of application of relevant control algorithms are included to illustrate their practical implementation. These examples are mainly taken from the area of marine technology with the multi-component external loading being represented as both varying in time and with magnitudes that are represented as statistical quantities. The relevant target group will be mechanical and structural engineers that are concerned with "smart components and structures" where optimal design principles and control actuators are combined. The book is also relevant for engineers e. g. involved in mechatronics and control applications.
Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE
by Nizar TouziThis book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.
Optimal Strategies in Sports Economics and Management
by Panos M. Pardalos Jaime Gil-Lafuente Sergiy ButenkoThis volume presents original contributions from renowned researchers in sports economics, management, and optimization.The book discusses up-to-date developments in several topics, including resource allocation strategies in sports industry, impact of the financial crisis on professional sports around the world, fairness in sports competitions, and optimization-based gambling strategies. "Optimal Strategies in Sports Economics and Management" will be of interest not only to students, researchers and practitioners involved with the sports industry, but also to the general public interested in sports such as soccer, hockey, American football, basketball, golf, and jai alai.
Optimal Surface Fitting of Point Clouds Using Local Refinement: Application to GIS Data (SpringerBriefs in Earth System Sciences)
by Tor Dokken Gaël Kermarrec Vibeke SkyttThis open access book provides insights into the novel Locally Refined B-spline (LR B-spline) surface format, which is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline surface has an overall smooth behavior and allows the modeling of local details with only a limited growth in data volume. In regions where many data points belong to the same smooth area, LR B-splines allow a very lean representation of the shape by locally adapting the resolution of the spline space to the size and local shape variations of the region. The iterative method can be modified to improve the accuracy in particular domains of a point cloud. The use of statistical information criterion can help determining the optimal threshold, the number of iterations to perform as well as some parameters of the underlying mathematical functions (degree of the splines, parameter representation). The resulting surfaces are well suited for analysis and computing secondary information such as contour curves and minimum and maximum points. Also deformation analysis are potential applications of fitting point clouds with LR B-splines.
Optimal Traffic Control: Urban Intersections
by Slobodan Guberinic Gordana Senborn Bratislav LazicDespite traffic circles, four-way stop signs, lights regulated by timers or sensors, and other methods, the management of urban intersections remains problematic. Consider that transportation systems have all the features of so-called complex systems: the great number of state and control variables, the presence of uncertainty and indeterminism, th
Optimal Trajectory Tracking of Nonlinear Dynamical Systems
by Jakob LöberBy establishing an alternative foundation of control theory, this thesis represents a significant advance in the theory of control systems, of interest to a broad range of scientists and engineers. While common control strategies for dynamical systems center on the system state as the object to be controlled, the approach developed here focuses on the state trajectory. The concept of precisely realizable trajectories identifies those trajectories that can be accurately achieved by applying appropriate control signals. The resulting simple expressions for the control signal lend themselves to immediate application in science and technology. The approach permits the generalization of many well-known results from the control theory of linear systems, e. g. the Kalman rank condition to nonlinear systems. The relationship between controllability, optimal control and trajectory tracking are clarified. Furthermore, the existence of linear structures underlying nonlinear optimal control is revealed, enabling the derivation of exact analytical solutions to an entire class of nonlinear optimal trajectory tracking problems. The clear and self-contained presentation focuses on a general and mathematically rigorous analysis of controlled dynamical systems. The concepts developed are visualized with the help of particular dynamical systems motivated by physics and chemistry.
Optimal Transport and Applications to Geometric Optics (SpringerBriefs on PDEs and Data Science)
by Cristian E. GutiérrezThis book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Ampère measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area. Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory and integration, as well as basic knowledge of functional analysis.
Optimal Transport for Applied Mathematicians
by Filippo SantambrogioThis monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.
Optimal Transport on Quantum Structures (Bolyai Society Mathematical Studies #29)
by Jan Maas Simone Rademacher Tamás Titkos Dániel VirosztekThe flourishing theory of classical optimal transport concerns mass transportation at minimal cost. This book introduces the reader to optimal transport on quantum structures, i.e., optimal transportation between quantum states and related non-commutative concepts of mass transportation. It contains lecture notes on classical optimal transport and Wasserstein gradient flowsdynamics and quantum optimal transportquantum couplings and many-body problemsquantum channels and qubits These notes are based on lectures given by the authors at the "Optimal Transport on Quantum Structures" School held at the Erdös Center in Budapest in the fall of 2022. The lecture notes are complemented by two survey chapters presenting the state of the art in different research areas of non-commutative optimal transport.
Optimale und adaptive Regelung technischer Systeme: Mathematische Grundlagen, praktisch relevante Beispiele und numerische Simulationen mit MATLAB®
by Anton BraunDieses Buch verschafft dem interessierten Leser an Hochschulen und Universitäten eine ideale Einführung in das anspruchsvolle Gebiet der optimalen Steuerung und Regelung dynamischer Systeme. Darüber hinaus werden dem Studierenden in einem separaten Kapitel die modernen Methoden der adaptiven Regelung technischer Prozesse nahegebracht, die vor allem für künftige Anwendungen von zentraler Bedeutung sind. Im Interesse eines möglichst bequemen Einstiegs in die zweifellos komplexe Materie bietet das Buch einen erschöpfenden Abriss der notwendigen mathematischen Grundlagen sowie zum Verständnis der diversen Kapitel eine Fülle praktisch relevanter Beispiele, untermauert mit den Methoden der aktuellen digitalen Simulationstechnik.
Optimality Conditions in Convex Optimization: A Finite-Dimensional View
by Joydeep Dutta Anulekha DharaOptimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literature-notably in the area of convex analysis-essential in developing many of the important results
Optimierung in C++: Grundlagen und Algorithmen
by Claus RichterDie Optimierung ist einer der bedeutendsten Zweige der Mathematik mit weitreichenden Anwendungen in der Statistik, Physik, Meteorologie bis hin zur Wirtschaft und Unternehmensforschung. Ziel der Optimierung ist eine Minimierung oder Maximierung der im jeweiligen System relevanten Parameter unter einschrankenden Nebenbedingungen. Praxisbezogen fuhrt Claus Richter in die Algorithmen der Optimierung ein. Einsteiger und Fortgeschrittene werden gleicherma?en auf den heutigen Stand der Dinge gebracht. In klaren Schritten umrei?t der Autor die Grundlagen dieses Gebietes, beginnend mit Definitionen und Optimalitatsbedingungen, um sich dann direkt an den C++-Programmierer zu wenden. Der notige mathematische Apparat, die verwendete Programmiersprache C++ und ihre Klassen werden vorgestellt. Damit stellt der Autor ein einheitliches Niveau her und wird so einer breiten Leserschaft gerecht. Im Folgenden werden 20 Verfahren der linearen, quadratischen und nichtlinearen Optimierung behandelt und dem Anwender nahergebracht. Jeder Algorithmus wird im Aufbau erlautert und an einem konkreten Beispiel demonstriert. Funf weitere Kapitel widmen sich anwendungsbezogenen Sachverhalten, u.a. der Parameteridentifikation, optimalen Steuerung und Strukturoptimierung. Durch die Bereitstellung der diskutierten Algorithmen und Beispiele als C++-Klassen gewahrleistet das Buch einen optimalen Einstieg in die Optimierung.
Optimierung mechanischer Strukturen
by Axel SchumacherZiel des Buches ist es, die notwendigen Kenntnisse für den effizienten Einsatz von mathematischen Optimierungsverfahren in der Strukturauslegung von Bauteilen zu vermitteln. Der Autor bezieht die neuesten Entwicklungen und Anwendungsbereiche auf dem Gebiet der Optimierung ein.
Optimierung mechanischer Strukturen: Grundlagen und industrielle Anwendungen
by Axel SchumacherZiel des Buches ist es, die notwendigen Kenntnisse für den effizienten Einsatz von mathematischen Optimierungsverfahren in der Strukturauslegung von Bauteilen zu vermitteln. Der Autor bezieht die neuesten Entwicklungen und Anwendungsbereiche auf dem Gebiet der Optimierung ein.
Optimierung von Versorgungsnetzen: Mathematische Modellierung und Lösungstechniken
by Lars Schewe Martin SchmidtWie funktioniert der deutsche Strommarkt? Wie bestimmt man die kostengünstigsten aber ausreichend großen Rohre für Wassernetze? Wie entscheidet man, ob bestimmte Mengen Erdgas durch ein Gasnetz transportiert werden können oder nicht? Dieses einführende Lehrbuch zeigt anhand konkreter Fragestellungen aus Strom-, Wasser-, Gas- und Verkehrsnetzen, mit welchen Begriffen und Techniken sich Transportvorgänge in solchen Versorgungsnetzen durch mathematische Modelle beschreiben lassen. Neben den technisch-physikalischen Modellen lernt der Leser Techniken zur Analyse typischer Märkte und Handelsmechanismen im Energiesektor kennen. Für beide Fälle werden die mathematischen Lösungsverfahren ausführlich diskutiert. Dazu werden unter anderem klassische Flusstheorie, Optimalitätsbedingungen, lineare Komplementaritätsprobleme und gemischt-ganzzahlige nichtlineare Optimierungsprobleme behandelt, so dass der Leser automatisch zentrale Tücken ganzzahliger und nichtlinearer Optimierungsprobleme kennenlernt und sich im Umgang mit diesen übt. Das Buch beinhaltet über 50 Übungsaufgaben sowie 5 Projektaufgaben, bei denen konkrete praktische Fragestellungen am Rechner gelöst werden sollen. Vorausgesetzt werden lediglich Vorkenntnisse aus den üblichen Grundvorlesungen der kontinuierlichen und linearen Optimierung (inklusive Dualität). Das Buch ist gut als Grundlage für eine Lehrveranstaltung im Umfang von 4 Semesterwochenstunden plus Übungen im Umfang von etwa 2 Semesterwochenstunden geeignet.
Optimierung: Einführung in mathematische Theorie und Methoden (Masterclass)
by Florian Jarre Josef StoerDieses Buch führt in die Theorie und Methoden der stetigen Optimierung ein und zeigt darüber hinaus einige Anwendungen aus der diskreten Optimierung: Als gängige Verfahren für lineare Programme werden die Simplex- und Innere-Punkte-Methode vorgestellt. Im Bereich der nichtrestringierten Optimierung werden neben deterministischen Abstiegsverfahren und Trust-Region-Verfahren auch stochastische Abstiegsverfahren analysiert, die etwa beim maschinellen Lernen zum Einsatz kommen. Nach einer detaillierten Betrachtung der Optimalitätsbedingungen für nichtlineare Optimierungsprobleme mit Nebenbedingungen folgt eine Analyse von Verfahren der erweiterten Lagrangefunktion und ADMM sowie von SQP-Verfahren. Der Hauptteil schließt mit einer Betrachtung von semidefiniten Programmen und deren Anwendungen. Für die zweite Auflage wurden zahlreiche Passagen überarbeitet und mehrere neue Abschnitte zu aktuellen Verfahren und Anwendungen ergänzt. Das Buch basiert auf einer zweisemestrigen Lehrveranstaltung der Autoren und enthält zahlreiche Übungsaufgaben. Es richtet sich an Leser, die Grundkenntnisse in Analysis, linearer Algebra und numerischer Mathematik mitbringen.
Optimisation Algorithms for Hand Posture Estimation (Algorithms for Intelligent Systems)
by Seyedali Mirjalili Shahrzad SaremiThis book reviews the literature on hand posture estimation using generative methods, identifying the current gaps, such as sensitivity to hand shapes, sensitivity to a good initial posture, difficult hand posture recovery in cases of loss in tracking, and lack of addressing multiple objectives to maximize accuracy and minimize computational cost. To fill these gaps, it proposes a new 3D hand model that combines the best features of the current 3D hand models in the literature. It also discusses the development of a hand shape optimization technique. To find the global optimum for the single-objective problem formulated, it improves and applies particle swarm optimization (PSO), one of the most highly regarded optimization algorithms and one that is used successfully in both science and industry. After formulating the problem, multi-objective particle swarm optimization (MOPSO) is employed to estimate the Pareto optimal front as the solution for this bi-objective problem. The book also demonstrates the effectiveness of the improved PSO in hand posture recovery in cases of tracking loss. Lastly, the book examines the formulation of hand posture estimation as a bi-objective problem for the first time.The case studies included feature 50 hand postures extracted from five standard datasets, and were used to benchmark the proposed 3D hand model, hand shape optimization, and hand posture recovery.
Optimisation convexe et inéquations variationnelles monotones (Mathématiques et Applications #89)
by Jean-Pierre Crouzeix Abdelhak Hassouni Eladio Ocaña-AnayaDe nombreux systèmes physiques, mécaniques, financiers et économiques peuvent être décrits par des modèles mathématiques qui visent à optimiser des fonctions, trouver des équilibres et effectuer des arbitrages. Souvent, la convexité des ensembles et des fonctions ainsi que les conditions de monotonie sur les systèmes d'inéquations qui régissent ces systèmes se présentent naturellement dans les modèles. C'est dans cet esprit que nous avons conçu ce livre en mettant l'accent sur une approche géométrique qui privilégie l'intuition par rapport à une approche plus analytique. Les démonstrations des résultats classiques ont été revues dans cette optique et simplifiées. De nombreux exemples d'applications sont étudiés et des exercices sont proposés.Ce livre s'adresse aux étudiants en master de mathématiques appliquées, ainsi qu'aux doctorants, chercheurs et ingénieurs souhaitant comprendre les fondements de l'analyse convexe et de la théorie des inéquations variationnelles monotones.
Optimisation in Synchromodal Logistics: From Theory to Practice (Lecture Notes in Operations Research)
by Frank PhillipsonThis book introduces the advances in synchromodal logistics and provides a framework to classify various optimisation problems in this field. It explores the application of this framework to solve a broad range of problems, such as problems with and without a central decision-maker, problems with and without full information, deterministic problems, problems coping with uncertainty, optimisation of a full network design problem. It covers theoretical constructs, such as discrete optimisation, robust optimisation, optimisation under uncertainty, multi-objective optimisation and agent based equilibrium models. Moreover, practical elaborated use cases are presented to deepen understanding. The book gives both researchers and practitioners a good overview of the field of synchromodal optimisation problems and offers the reader practical methods for modelling and problem-solving.
Optimised Projections for the Ab Initio Simulation of Large and Strongly Correlated Systems
by David D. O'ReganDensity functional theory (DFT) has become the standard workhorse for quantum mechanical simulations as it offers a good compromise between accuracy and computational cost. However, there are many important systems for which DFT performs very poorly, most notably strongly-correlated materials, resulting in a significant recent growth in interest in 'beyond DFT' methods. The widely used DFT+U technique, in particular, involves the addition of explicit Coulomb repulsion terms to reproduce the physics of spatially-localised electronic subspaces. The magnitude of these corrective terms, measured by the famous Hubbard U parameter, has received much attention but less so for the projections used to delineate these subspaces. The dependence on the choice of these projections is studied in detail here and a method to overcome this ambiguity in DFT+U, by self-consistently determining the projections, is introduced. The author shows how nonorthogonal representations for electronic states may be used to construct these projections and, furthermore, how DFT+U may be implemented with a linearly increasing cost with respect to system size. The use of nonorthogonal functions in the context of electronic structure calculations is extensively discussed and clarified, with new interpretations and results, and, on this topic, this work may serve as a reference for future workers in the field.
Optimization
by Kenneth LangeFinite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students' skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications. In this second edition the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions.
Optimization Algorithms for Distributed Machine Learning (Synthesis Lectures on Learning, Networks, and Algorithms)
by Gauri JoshiThis book discusses state-of-the-art stochastic optimization algorithms for distributed machine learning and analyzes their convergence speed. The book first introduces stochastic gradient descent (SGD) and its distributed version, synchronous SGD, where the task of computing gradients is divided across several worker nodes. The author discusses several algorithms that improve the scalability and communication efficiency of synchronous SGD, such as asynchronous SGD, local-update SGD, quantized and sparsified SGD, and decentralized SGD. For each of these algorithms, the book analyzes its error versus iterations convergence, and the runtime spent per iteration. The author shows that each of these strategies to reduce communication or synchronization delays encounters a fundamental trade-off between error and runtime.
Optimization Algorithms for Networks and Graphs
by James EvansA revised and expanded advanced-undergraduate/graduate text (first ed., 1978) about optimization algorithms for problems that can be formulated on graphs and networks. This edition provides many new applications and algorithms while maintaining the classic foundations on which contemporary algorithm