Optimalisering

This monograph presents the most recent developments in the study of Hamilton-Jacobi Equations and control problems with discontinuities, mainly from the viewpoint of partial differential equations. Two main cases are investigated in detail: the case of codimension 1 discontinuities and the stratified case in which the discontinuities can be of any codimensions. In both, connections with deterministic control problems are carefully studied, and numerous examples and applications are illustrated throughout the text.After an initial section that provides a ¿toolbox¿ containing key results which will be used throughout the text, Parts II and III completely describe several recently introduced approaches to treat problems involving either codimension 1 discontinuities or networks. The remaining sections are concerned with stratified problems either in the whole space R^N or in bounded or unbounded domains with state-constraints. In particular, the use of stratified solutions to treat problems with boundary conditions, where both the boundary may be non-smooth and the data may present discontinuities, is developed. Many applications to concrete problems are explored throughout the text ¿ such as Kolmogorov-Petrovsky-Piskunov (KPP) type problems, large deviations, level-sets approach, large time behavior, and homogenization ¿ and several key open problems are presented.This monograph will be of interest to graduate students and researchers working in deterministic control problems and Hamilton-Jacobi Equations, network problems, or scalar conservation laws.

Each of the "Keys to the Kingdom" Advanced Training Course Manuals will further a Seekers reach on the Pathway leading out of this Universe.

Each of the "Keys to the Kingdom" Advanced Training Course Manuals will further a Seekers reach on the Pathway leading out of this Universe.

This book offers a comprehensive introduction to technological advances in Internet of Vehicles (IoV), including vehicular communications, vehicular system architectures, data dissemination algorithms, resource allocation schemes, and AI-enabled applications. It focuses on the state-of-the-art IoV with regard to three major directions, namely networking, cooperation, and intelligence, including advanced wireless communication technologies, algorithm theory, optimization mechanisms, and AI technologies. In addition, the book includes a number of case studies with system prototype implementation and hands-on experiments in IoV, making it suitable both as a technical reference work for professionals and as a textbook for graduate students.

"Get up-to-speed with the fundamentals of how electricity markets are structured and operated with this comprehensive textbook, requiring no prior experience in power systems or energy economics. An ideal introduction for senior undergraduate and graduate students in electrical engineering, economics, and operations research"--

This book introduces the fundamentals of probability, statistical, and reliability concepts, the classical methods of uncertainty quantification and analytical reliability analysis, and the state-of-the-art approaches of design optimization under uncertainty (e.g., reliability-based design optimization and robust design optimization). The topics include basic concepts of probability and distributions, uncertainty quantification using probabilistic methods, classical reliability analysis methods, time-variant reliability analysis methods, fundamentals of deterministic design optimization, reliability-based design optimization, robust design optimization, other methods of design optimization under uncertainty, and engineering applications of design optimization under uncertainty.

This proceedings volume gathers selected, blinded peer-reviewed contributions presented at the XXIX International Joint Conference on Industrial Engineering and Operations Management (IJCIEOM), held in Lisbon, Portugal, from June 28th to 30th, 2023.This volume focuses especially on the applications of Industrial Engineering and Operations Management for research and practice. It includes relevant information for academics since most of the chapters focus on real-world case studies and systematic reviews. It also provides valuable insights for professionals in the industrial sector by presenting solutions to complex industrial challenges.The 2023 iteration of the IJCIEOM conference had the theme "Developing resilience in Industrial Engineering and Operations Management" and aimed to analyze the resilience of supply chains in the post-COVID-19 era. The works published in this volume focus on how Digital Transformation (DX) and Artificial Intelligence (AI) have made themanufacturing and service industry more resistant to VUCA elements (i.e., volatile, uncertain, complex, and ambiguous). Regarding DX and AI, the research specifically focused on supply chain management, project management, and Industry 4.0. Other studies explore how industrial engineering incorporated innovative and technological concepts into service and product operations. Overall, this volume provides a valuable resource for researchers and practitioners alike as it presents numerous relevant contributions in identifying new challenges and opportunities for industrial engineering and operations management.This conference was sponsored by renowned international industry engineering associations, particularly the American Society for Engineering Management (ASEM), the Institute of Industrial & Systems Engineers (IISE), and the Asociación para el Desarrollo de la Ingeniería de Organización (ADINGOR).

This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present.Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality andthe Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of ¿-convergence.While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.

An introduction to game theory, complete with step-by-step tools and detailed examples. This book offers condensed breakdowns of game-theory concepts. Specifically, this textbook provides ¿tools¿ or ¿recipes¿ to solve different classes of games. Game Theory presents the information as plainly and clearly as possible. Every chapter begins with the main definitions and concepts before diving into the applications to different settings across economics, business, and other social sciences. Chapters walk readers through algebraic steps and simplifications. This makes the text accessible for undergraduate and Masters-level students in economics and finance. Paired with the exercises published on the accompanying website, students will improve both their theoretical and practical understandings of game theory. Readers will walk away from this book understanding complete and incomplete information models as well as signaling games.

This book presents the best papers from the 4th International Conference on Mathematical Research for Blockchain Economy (MARBLE) 2023, held in London, UK. While most blockchain conferences and forums are dedicated to business applications, product development, or Initial Coin Offering (ICO) launches, this conference focused on the mathematics behind blockchain to bridge the gap between practice and theory.The book spans the divide between theoretical promise and practical reality in blockchain technology and explores the challenges hindering its real-world integration across diverse sectors, offering comprehensive insights into issues like scalability, security, and privacy.

This book offers a careful selection of studies in optimization techniques based on artificial intelligence, applied to inverse problems in radiative transfer. In this book, the reader will find an in-depth exploration of heuristic optimization methods, each meticulously described and accompanied by historical context and natural process analogies.From simulated annealing and genetic algorithms to artificial neural networks, ant colony optimization, and particle swarms, this volume presents a wide range of heuristic methods. Additional approaches such as generalized extreme optimization, particle collision, differential evolution, Luus-Jaakola, and firefly algorithms are also discussed, providing a rich repertoire of tools for tackling challenging problems.While the applications showcased primarily focus on radiative transfer, their potential extends to various domains, particularly nonlinear and large-scale problems where traditional deterministic methods fall short. With clear and comprehensive presentations, this book empowers readers to adapt each method to their specific needs. Furthermore, practical examples of classical optimization problems and application suggestions are included to enhance your understanding.This book is suitable to any researcher or practitioner whose interests lie on optimization techniques based in artificial intelligence and bio-inspired algorithms, in fields like Applied Mathematics, Engineering, Computing, and cross-disciplinary areas.

This 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.

This study guide is designed for students taking a Calculus III course. The textbook includes examples, questions, and practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The material covered in the book includes linear algebra and analytical geometry; lines, surfaces, and vector functions in three-dimensional coordinate systems; multiple-variable functions; multiple integrals and their applications; line integrals and their applications. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve students¿ problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based courses.

This book deals with the first discriminant theory of linearly separable data (LSD), Theory3, based on the four ordinary LSD of Theory1 and 169 microarrays (LSD) of Theory2. Furthermore, you can quickly analyze the medical data with the misclassified patients which is the true purpose of diagnoses. Author developed RIP (Optimal-linear discriminant function finding the combinatorial optimal solution) as Theory1 in decades ago, that found the minimum misclassifications. RIP discriminated 63 (=26¿1) models of Swiss banknote (200*6) and found the minimum LSD: basic gene set (BGS). In Theory2, RIP discriminated Shipp microarray (77*7129) which was LSD and had only 32 nonzero coefficients (first Small Matryoshka; SM1). Because RIP discriminated another 7,097 genes and found SM2, the author developed the Matryoshka feature selection Method 2 (Program 3), that splits microarray into many SMs. Program4 can split microarray into many BGSs. Then, the wide columnLSD (Revolution-0), such as microarray (n5) models, including BGS, become LSD among (219¿1) models. Because Program2 confirms BGS has the minimum average error rate, BGS is the most compact and best model satisfying Occam¿s Razor. With this book, physicians obtain complete diagnostic results for disease, and engineers can become a true data scientist, by obtaining integral knowledge ofstatistics and mathematical programming with simple programs.

This edited book discusses creative and recent developments of fuzzy systems and its real-life applications of multiple criteria decision making. Keeping on the existing fuzzy sets and recent developed fuzzy sets, viz., intuitionistic fuzzy, Pythagorean fuzzy, Fermatean fuzzy, Hesitant fuzzy and multiple criteria decision approaches, this book is committed to probing the soft computing techniques and fuzzy multiple criteria decision making in favour of fuzzy intelligent system and business analytics. It also addresses novel development of fuzzy set theory as well as real-life applications of fuzzy systems. It presents challenging and useful real-world applications based on problems of decision making in various fields. The modelling and solution procedures of such real-world problems will be provided concisely although all topics start with a more developed resolution. The contributory chapters will be based on the vast research experiences of the authors in real-world decision-making problems. This book provides readers with a valuable conspectus of several decision-making problems as a reference for researchers and industrial practitioners in this field. This book will broadly cover recent development of fuzzy systems and its applications of multiple criteria decision making in the areas of management and production, manufacturing management, selections problems, group decision making, transportation and logistics, inventory control systems and interval technique/fuzzy technique (uncertainty) of the above mentioned areas.

Each 'Professional Course' lesson-booklet offers simple exercises and techniques that directly apply the philosophy of Systemology to increase your true knowingness and improve your capabilities in this life.

This monograph explores the analysis and design of model-free optimal control systems based on reinforcement learning (RL) theory, presenting new methods that overcome recent challenges faced by RL.  New developments in the design of sensor data efficient RL algorithms are demonstrated that not only reduce the requirement of sensors by means of output feedback, but also ensure optimality and stability guarantees.  A variety of practical challenges are considered, including disturbance rejection, control constraints, and communication delays.  Ideas from game theory are incorporated to solve output feedback disturbance rejection problems, and the concepts of low gain feedback control are employed to develop RL controllers that achieve global stability under control constraints.Output Feedback Reinforcement Learning Control for Linear Systems will be a valuable reference for graduate students, control theorists working on optimal control systems, engineers, and applied mathematicians.

This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed.Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems - handy for understanding and self-study - and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume.By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.

After providing an in-depth introduction to derivative-free global optimization with various constraints, this book presents new original results from well-known experts on the subject. A primary focus of this book is the well-known class of deterministic DIRECT (DIviding RECTangle)-type algorithms. This book describes a new set of algorithms derived from newly developed partitioning, sampling, and selection approaches in the box- and generally-constrained global optimization, including extensions to multi-objective optimization. DIRECT-type optimization algorithms are discussed in terms of fundamental principles, potential, and boundaries of their applicability. The algorithms are analyzed from various perspectives to offer insight into their main features. This explains how and why they are effective at solving optimization problems. As part of this book, the authors also present several techniques for accelerating the DIRECT-type algorithms through parallelization and implementing efficient data structures by revealing the pros and cons of the design challenges involved. A collection of DIRECT-type algorithms described and analyzed in this book is available in DIRECTGO, a MATLAB toolbox on GitHub. Lastly, the authors demonstrate the performance of the algorithms for solving a wide range of global optimization problems with various constraints ranging from a few to hundreds of variables.Additionally, well-known practical problems from the literature are used to demonstrate the effectiveness of the developed algorithms. It is evident from these numerical results that the newly developed approaches are capable of solving problems with a wide variety of structures and complexity levels.Since implementations of the algorithms are publicly available, this monograph is full of examples showing how to use them and how to choose the most efficient ones, depending on the nature of the problem being solved. Therefore, many specialists, students, researchers, engineers, economists, computer scientists, operations researchers, and others will find this book interesting and helpful.

This book gathers peer-reviewed contributions submitted to the 21st European Conference on Mathematics for Industry, ECMI 2021, which was virtually held online, hosted by the University of Wuppertal, Germany, from April 13th to April 15th, 2021. The works explore mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Topics covered include: Applied Physics, Biology and Medicine, Cybersecurity, Data Science, Economics, Finance and Insurance, Energy, Production Systems, Social Challenges, and Vehicles and Transportation.The goal of the European Consortium for Mathematics in Industry (ECMI) conference series is to promote interaction between academia and industry, leading to innovations in both fields. These events have attracted leading experts from business, science and academia, and have promoted the application of novel mathematical technologies to industry. They have also encouraged industrial sectors to share challenging problems where mathematicians can provide fresh insights and perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.

This textbook provides a comprehensive overview of noncooperative and cooperative dynamic games involving uncertain parameter values, with the stochastic process being described by an event tree. Primarily intended for graduate students of economics, management science and engineering, the book is self-contained, as it defines and illustrates all relevant concepts originally introduced in static games before extending them to a dynamic framework. It subsequently addresses the sustainability of cooperative contracts over time and introduces a range of mechanisms to help avoid such agreements breaking down before reaching maturity. To illustrate the concepts discussed, the book provides various examples of how dynamic games played over event trees can be applied to environmental economics, management science, and engineering.

This interesting book discusses why, as an activity, topic and metaphor, play and game have become an integral part of modern life. Empirically exemplary and theoretically grounded, this book discusses the developments and expansions in gaming, from easily accessible casual games to the galaxy-spanning gaming worlds of Massively Multiplayer Online Role-Playing Games (MMORPGs). It shows how gaming has become a focal point of the entertainment industry, marked by boundless professionalization and monetization, especially in the realm of sports, and how games become global platforms for social networks, where players from all over the world meet in digital sandboxes. The combination of the virtual and the ludic creates hyperreal spaces in which people try out new forms of interaction, cooperation, and even brainstorming. The authors ask if this behavior has become the new way of life and the new normal, and if this heralds the ludic century. They take readers on a journey to understand the dynamics of today's gaming society, and base their observations and analyses on an original theory of play, which, in contrast to social normalcy, revolves around the allure and threats of the unexpected. This book is of interest to students and researchers of social science and communication studies, especially those working on the interface of AI and society.

Based on over 15 years¿ experience in the design and delivery of successful first-year courses, this book equips undergraduates with the mathematical skills required for degree courses in economics, finance, management, and business studies. The book starts with a summary of basic skills and takes its readers as far as constrained optimisation helping them to become confident and competent in the use of mathematical tools and techniques that can be applied to a range of problems in economics and finance.Designed as both a course text and a handbook, the book assumes little prior mathematical knowledge beyond elementary algebra and is therefore suitable for students returning to mathematics after a long break. The fundamental ideas are described in the simplest mathematical terms, highlighting threads of common mathematical theory in the various topics.Features of the book include:a systematic approach: ideas are touched upon, introduced gradually and thenconsolidated through the use of illustrative examples;several entry points to accommodate differing mathematical backgrounds; numerous problems, with full solutions, and exercises to illustrate the theory and applications; key learning objectives and self-assessment questions provided for each chapter; full solutions to exercises, available to lecturers via the Springer Nature Extramaterial - Lecturer Material website. Vass Mavron is Emeritus Professor of Mathematics at Aberystwyth University. Tim Phillips is Professor of Applied Mathematics in the School of Mathematics at Cardiff University.

This book is the first comprehensive guide to logic-based Benders decomposition (LBBD), a general and versatile method for breaking large, complex optimization problems into components that are small enough for practical solution. The author introduces logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method. It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems. On the theoretical side, this book provides a full account of inference duality concepts that underlie LBBD, as well as a description of how LBBD can be combined with stochastic and robust optimization, heuristic methods, and decision diagrams. It also clarifies the connection between LBBD and combinatorial Benders cuts for mixed integer programming. On the practical side, it explains how LBBD has been applied to a rapidly growingvariety of problem domains. After describing basic theory, this book provides a comprehensive review of the rapidly growing literature that describes these applications, in each case explaining how LBBD is adapted to the problem at hand. In doing so this work provides a sourcebook of ideas for applying LBBD to new problems as they arise.

This open access book gives a systematic introduction into the spectral theory of differential operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph.The book has two central themes: the trace formula and inverse problems.The trace formula is relating the spectrum to the set of periodic orbits and is comparable to the celebrated Selberg and Chazarain-Duistermaat-Guillemin-Melrose trace formulas. Unexpectedly this formula allows one to construct non-trivial crystalline measures and Fourier quasicrystals solving one of the long-standing problems in Fourier analysis. The remarkable story of this mathematical odyssey is presented in the first part of the book.To solve the inverse problem for Schrödinger operators on metric graphs the magnetic boundary control method is introduced. Spectral data depending on the magnetic flux allow one to solve the inverse problem in full generality, this means to reconstruct not only the potential on a given graph, but also the underlying graph itself and the vertex conditions.The book provides an excellent example of recent studies where the interplay between different fields like operator theory, algebraic geometry and number theory, leads to unexpected and sound mathematical results. The book is thought as a graduate course book where every chapter is suitable for a separate lecture and includes problems for home studies. Numerous illuminating examples make it easier to understand new concepts and develop the necessary intuition for further studies.

This book introduces a maintenance model that will assist decision-makers in their choice of building maintenance policies. The model is stochastic and condition-based that analyses the impact of different maintenance strategies on the durability and performance of different buildings envelope elements (facades, windows, and roofs).  As non-structural elements, the maintenance of buildings envelope can be disregarded stakeholders. However, as first barrier to the external environment, these elements are critical to buildings' overall performance and are expected to meet aesthetic, comfort, safety, and durability requirements. The methodology presented is innovative. The maintenance model is based on a Petri net formalism and includes degradation, inspection, maintenance, and renewal processes. The model provides key information, such as: i) the impact of different maintenance strategies on the service life and durability of the building components; ii) the impact of maintenance on their performance over time; iii) the life cycle costs; and iv) the impact of maintenance on the buildings' use.  The book will be of use to a variety of professionals in the construction sector.

This handbook aims to serve as a one-stop, reliable source of reference, with curations of survey and expository contributions on the state-of-the-art in Blockchain technology. It covers a comprehensive range of topics, providing the technical and non-technical reader with fundamentals, applications, and deep details on a variety of topics. The readership is expected to span broadly from technologically-minded business professionals and entrepreneurs, to students, instructors, novices and seasoned researchers, in computer science, engineering, software engineering, finance, and data science. Though Blockchain technology is relatively young, its evolution as a field and a practice is booming in growth and its importance to society had never been more important than it is today. Blockchain solutions enable a decentralization of a digital society where people can contribute, collaborate, and transact without having to second-guess the trust and transparency factors with many geographical, financial, and political barriers removed. It is the distributed ledger technology behind the success of Bitcoin, Ethereum, and many emerging applications.The resource is divided into 5 parts. Part 1 (Foundation) walks the reader through a comprehensive set of essential concepts, protocols, and algorithms that lay the foundation for Blockchain. Part 2 (Scalability) focuses on the most pressing challenges of today's blockchain networks in how to keep pace with real-world expectations. Part 3 (Trust and Security) provides detailed coverage on the issues of trust, reputation, and security in Blockchain.  Part 4 (Decentralized Finance) is devoted to a high-impact application of Blockchain to finance, the sector that has most benefitted from this technology. Part 5 (Application and Policy) includes several cases where Blockchain applies to the real world.

This monograph introduces a novel multiset-based conceptual, mathematical and knowledge engineering paradigm, called multigrammatical framework (MGF), used for planning and scheduling in resource-consuming, resource-producing (industrial) and resource-distributing (economical) sociotechnological systems (STS). This framework is meant to enable smart operation not only in a "e;business-as-usual"e; mode, but also in extraordinary, highly volatile or hazardous environments. It is the result of convergence and deep integration into a unified, flexible and effectively implemented formalism operating on multisets of several well-known paradigms from classical operations research and modern knowledge engineering, such as: mathematical programming, game theory, optimal scheduling, logic programming and constraint programming. The mathematical background needed for MGF, its algorithmics, applications, implementation issues, as well as its nexus with known models from operations research and theoretical computer science areas are considered. The resilience and recovery issues of an STS are studied by applying the MGF toolkit and on paying special attention to the multigrammatical assessment of resilience of energy infrastructures. MGF-represented resource-based games are introduced, and directions for further development are discussed. The author presents multiple applications to business intelligence, critical infrastructure, ecology, economy and industry. This book is addressed to scholars working in the areas of theoretical and applied computer science, artificial intelligence, systems analysis, operations research, mathematical economy and critical infrastructure protection, to engineers developing software-intensive solutions for implementation of the knowledge-based digital economy and Industry 4.0, as well as to students, aspirants and university staff. Foundational knowledge of set theory, mathematical logic and routine operations on data bases is needed to read this book. The content of the monograph is gradually presented, from simple to complex, in a well-understandable step-by-step manner. Multiple examples and accompanying figures are included in order to support the explanation of the various notions, expressions and algorithms.