Optimalisering

This book introduces the Learning-Augmented Network Optimization (LANO) paradigm, which interconnects network optimization with the emerging AI theory and algorithms and has been receiving a growing attention in network research. The authors present the topic based on a general stochastic network optimization model, and review several important theoretical tools that are widely adopted in network research, including convex optimization, the drift method, and mean-field analysis. The book then covers several popular learning-based methods, i.e., learning-augmented drift, multi-armed bandit and reinforcement learning, along with applications in networks where the techniques have been successfully applied. The authors also provide a discussion on potential future directions and challenges.

De 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.

Machine learning heavily relies on optimization algorithms to solve its learning models. Constrained problems constitute a major type of optimization problem, and the alternating direction method of multipliers (ADMM) is a commonly used algorithm to solve constrained problems, especially linearly constrained ones. Written by experts in machine learning and optimization, this is the first book providing a state-of-the-art review on ADMM under various scenarios, including deterministic and convex optimization, nonconvex optimization, stochastic optimization, and distributed optimization. Offering a rich blend of ideas, theories and proofs, the book is up-to-date and self-contained. It is an excellent reference book for users who are seeking a relatively universal algorithm for constrained problems. Graduate students or researchers can read it to grasp the frontiers of ADMM in machine learning in a short period of time.

This comprehensive book brings together the latest developments in reliability and maintainability methods from leading research groups globally. Covering a diverse range of subject areas, from mechanical systems to cyber-physical systems, the book offers both theoretical advancements and practical applications in various industries. With a focus on reliability modelling, reliability analysis, reliability design, maintenance optimization, warranty policy, prognostics and health management, this book appeals to academic and industrial professionals in the field of reliability engineering and beyond. It features real-world case studies from turbofan engines bearings, industrial robots, wireless networks, aircraft actuation systems, and more. This book is ideal for engineers, scientists, and graduate students in reliability, maintainability, design optimization, prognostics and health management, and applied probability and statistics.

Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for several classes of functional fractional difference equations and inclusions. Covered equations include delay effects of finite, infinite, or state-dependent nature, and tools used to establish the existence results for the proposed problems include fixed point theorems, densifiability techniques, monotone iterative technique, notions of Ulam stability, attractivity and the measure of non-compactness, as well as the measure of weak noncompactness. The tools of fractional calculus are found to be of great utility in improving the mathematical modeling of many natural phenomena and processes occurring in the areas of engineering, social, natural, and biomedical sciences. All abstract results in the book are illustrated by examples in applied mathematics, engineering, biomedical, and other applied sciences.

This book constitutes the refereed proceedings of the 23rd International Conference on Group Decision and Negotiation, GDN 2023, which took place in Tokyo, Japan during June 11¿15, 2023.The field of Group Decision and Negotiation focuses on decision processes with at least two participants and a common goal but conflicting individual goals. Research areas of Group Decision and Negotiation include electronic negotiations, experiments, the role of emotions in group decision and negotiations, preference elicitation and decision support for group decisions and negotiations, and conflict resolution principles. This year¿s conference focusses on multimodal interactions.The 11 full papers presented in this volume were carefully reviewed and selected from 102 submissions. They were organized in the following topical sections: Taking a step back: Critically re-examining technology interactions with group decision and negotiation; preference modeling and multi-criteria decision-making;and conflict modeling and distributive mechanisms.

This book is addressed to researchers in operations research, data science and artificial intelligence. It collects selected contributions from the first hybrid "e;Optimization and Decision Science - ODS2021"e; international conference on the theme Optimization and Artificial Intelligence and Data Sciences, which was held in Rome 14-17 September 2021 and organized by AIRO, the Italian Operations Research Society and the Department of Statistical Sciences of Sapienza University of Rome. The book offers new and original contributions on different methodological optimization topics, from Support Vector Machines to Game Theory Network Models, from Mathematical Programming to Heuristic Algorithms, and Optimization Methods for a number of emerging problems from Truck and Drone delivery to Risk Assessment, from Power Networks Design to Portfolio Optimization. The articles in the book can give a significant edge to the general themes of sustainability and pollution reduction, distributive logistics, healthcare management in pandemic scenarios and clinical trials, distributed computing, scheduling, and many others. For these reasons, the book is aimed not only at researchers in the Operations Research community but also for practitioners facing decision-making problems in these areas and to students and researchers from other disciplines, including Artificial Intelligence, Computer Sciences, Finance, Mathematics, and Engineering.

This volume presents the revised papers of the 14th International Conference in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2020, which took place online during August 10-14, 2020. This book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in statistics, machine learning, finance, and computer graphics, offering information on the latest developments in Monte Carlo and quasi-Monte Carlo methods and their randomized versions.

This edited book reviews the intertwining disciplines of nature-inspired optimization algorithms and bio-inspired soft-computing for real world applications, with the interaction between metaheuristics with complex systems. The authors present methods and techniques in IoT, image processing, smart manufacturing and healthcare.

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems.  Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.

As global CO2 emissions continue to rise, the need to limit global warming has become an increasingly critical scientific and political challenge. The conversion of airport apron vehicles from combustion engines to electric drives is a promising technology in the aviation sector to reduce emissions. However, electric vehicles require longer recharge times, which can be overcome by implementing Dynamic Inductive Charging (DIC) technology. DIC enables charging while driving and provides vehicles with almost unlimited driving range. This book explores different approaches to optimizing the allocation of the required DIC infrastructure components by developing mathematical optimization models and algorithms.

The COVID-19 pandemic is not only a threat to our health and economy, but also has strong implications for defence and security. Indeed, defence leaders have highlighted a second fight surrounding the spread of COVID-19, namely disinformation and preparing to face adversaries willing to exploit the public health crisis for nefarious purposes. The current pandemic is a breeding ground for the propagation of disinformation, as it represents the first major global health event in which large social media platforms have become the main distributor of information. This multi-national edited volume consists of contributions from Defence Science, academia and industry, including NATO Headquarters, United States, Netherlands, Singapore, United Kingdom and Norway. The content is aimed at a diverse audience, including NATO members, researchers from defence and security organizations, academics, and militaries including analysts and practitioners, as well as policy makers. This volume focuses on various aspects of COVID-19 disinformation, including identifying global dominant disinformation narratives and the methods used to spread disinformation, examining COVID-19 disinformation within the broader context of the cognitive domain, examining the psychological effects of COVID-19 disinformation and COVID-19 disinformation on instant messaging platforms, along with examining various countermeasures to disinformation.

This book presents a comprehensive analysis of stability, stabilization, and fault detection in networked control systems, with a focus on unmanned marine vehicles. It investigates the challenges of network-based control in areas like heading control, fault detection filter and controller design, dynamic positioning, and cooperative target tracking. Communication networks in control systems can induce delays and dropouts, so the book presents the importance of stability analysis, stabilize, and fault detection. To help readers gain a deeper understanding of these concepts, the book provides fundamental concepts and real-world examples.This book is a valuable resource for researchers and practitioners working in the field of network-based control for unmanned marine vehicles.

In this book, a risk management approach starts off by discussing important issues related to managing supply chain disruption risks from various perspectives during VUCA times. It explores the essence and principles relating to managing these risks and provides the framework and multi-goal model groups for managing such unknown-unknown risks and subsequent disruptions at a global scale.The book explores and presents the latest developments across different emerging topics in supply chain risk and disruption management. These include (i) an overview of supply chain risk, and disruption management tools, techniques, and approaches, (ii) a review on uncertainty modeling for decentralized supply chain systems, (iii) supply chain deep uncertainties and risks - the 'new normal', (iv) emergent technologies for supply chain risk and disruption management, (v) supply chain resilience strategies for times of unprecedented uncertainty, (vi) the role of blockchain in developing supply chain resilience against disruptions, (vii) a qualitative study on supply chain risk management adopting blockchain technology, (viii) assessment of risks and risk management for agriculture supply chain, (ix) resilience of agri-food supply chains: Australian developments after a decade of supply and demand shocks, (x) prioritization of risks in the pharmaceutical supply chains (xi) improving medical supply chain disruption management with the blockchain technology, and (xii) impacts of resilience practices on supply chain sustainability.The book contributes significantly to the growing body of knowledge concerning the theory and practice of managing supply chain risks and disruptions in strategic management, operations and supply chain, and sustainability literature. It presents contemporary, innovative and latest developments in applying smart management tools, techniques and approaches for managing supply chain risk and disruption and future-proofing supply chains to become agile, resilient and sustainable.

This monograph considers the analytical and geometrical questions emerging from the study of thin elastic films that exhibit residual stress at free equilibria. It provides the comprehensive account, the details and background on the most recent results in the combined research perspective on the classical themes: in Differential Geometry ¿ that of isometrically embedding a shape with a given metric in an ambient space of possibly different dimension, and in Calculus of Variations ¿ that of minimizing non-convex energy functionals parametrized by a quantity in whose limit the functionals become degenerate.Prestressed thin films are present in many contexts and applications, such as: growing tissues, plastically strained sheets, engineered swelling or shrinking gels, petals and leaves of flowers, or atomically thin graphene layers. While the related questions about the physical basis for shape formation lie at the intersection of biology, chemistry and physics, fundamentally they are of the analytical and geometrical character, and can be tackled using the techniques of the dimension reduction, laid out in this book.The text will appeal to mathematicians and graduate students working in the fields of Analysis, Calculus of Variations, Partial Differential Equations, and Applied Math. It will also be of interest to researchers and graduate students in Engineering (especially fields related to Solid Mechanics and Materials Science), who would like to gain the modern mathematical insight and learn the necessary tools.

This book is devoted to the study of the turnpike phenomenon arising in optimal control theory. Special focus is placed on Turnpike results, in sufficient and necessary conditions for the turnpike phenomenon and in its stability under small perturbations of objective functions. The most important feature of this book is that it develops a large, general class of optimal control problems in metric space. Additional value is in the provision of solutions to a number of difficult and interesting problems in optimal control theory in metric spaces. Mathematicians working in optimal control, optimization, and experts in applications of optimal control to economics and engineering, will find this book particularly useful.All main results obtained in the book are new. The monograph contains nine chapters. Chapter 1 is an introduction. Chapter 2 discusses Banach space valued functions, set-valued mappings in infinite dimensional spaces, and related continuous-time dynamical systems. Some convergence results are obtained. In Chapter 3, a discrete-time dynamical system with a Lyapunov function in a metric space induced by a set-valued mapping, is studied. Chapter 4 is devoted to the study of a class of continuous-time dynamical systems, an analog of the class of discrete-time dynamical systems considered in Chapter 3. Chapter 5 develops a turnpike theory for a class of general dynamical systems in a metric space with a Lyapunov function. Chapter 6 contains a study of the turnpike phenomenon for discrete-time nonautonomous problems on subintervals of half-axis in metric spaces, which are not necessarily compact. Chapter 7 contains preliminaries which are needed in order to study turnpike properties of infinite-dimensional optimal control problems. In Chapter 8, sufficient and necessary conditions for the turnpike phenomenon for continuous-time optimal control problems on subintervals of the half-axis in metric spaces, is established. In Chapter 9, the examination continues of the turnpike phenomenon for the continuous-time optimal control problems on subintervals of half-axis in metric spaces discussed in Chapter 8.

"This is a graduate-level introduction to the key ideas and theoretical foundation of the vibrant field of optimal mass transport in the Euclidean setting. Taking a pedagogical approach, it introduces concepts gradually and in an accessible way, while also remaining technically and conceptually complete"--

This richly illustrated book introduces the subject of optimization to a broad audience with a balanced treatment of theory, models and algorithms. Through numerous examples from statistical learning, operations research, engineering, finance and economics, the text explains how to formulate and justify models while accounting for real-world considerations such as data uncertainty. It goes beyond the classical topics of linear, nonlinear and convex programming and deals with nonconvex and nonsmooth problems as well as games, generalized equations and stochastic optimization.The book teaches theoretical aspects in the context of concrete problems, which makes it an accessible onramp to variational analysis, integral functions and approximation theory. More than 100 exercises and 200 fully developed examples illustrate the application of the concepts. Readers should have some foundation in differential calculus and linear algebra. Exposure to real analysiswould be helpful but is not prerequisite.

This textbook introduces Artificial Intelligence (AI) techniques for wireless communications and networks, helping readers to find solutions for communications and network problems using AI.Artificial Intelligence for 6G introduces, in a step-by-step manner, AI techniques such as:unsupervised learning;supervised learning;reinforcement learning; anddeep learning.It explains how these techniques can be used for wireless communications and network systems, particularly in designing and optimizing 6G networks.This book is at the forefront of 6G research, and will be of interest internationally, to graduate students, academics, engineers, and developers who are focused on future development of network systems and mobile communications. 

This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. The author demonstrates how this method can be utilized as a convenient tool for proving the existence of these solutions when others may fail, such as in cases of evolution equations with nonautonomous operators, with low regular data, or with singular diffusion coefficients. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation. This procedure simplifies the proof of the existence of minimizers and, in particular, the determination of the first-order conditions of optimality. The dual variational formulation is illustrated in the text with specific diffusion equations that have general nonlinearities provided by potentials having various stronger or weaker properties. These equations can represent mathematical modelsto various real-world physical processes. Inverse problems and optimal control problems are also considered, as this technique is useful in their treatment as well.

This volume comprises papers from the 18th Conference on Systems Engineering Research (CSER). The theme of this volume, "e;Recent Trends and Advances in Model-Based Systems Engineering,"e; reflects the fact that systems engineering is undergoing a transformation motivated by mission and system complexity and enabled by technological advances such as model-based systems engineering, digital engineering, and the convergence of systems engineering with other disciplines. This conference is focused on exploring recent trends and advances in model-based systems engineering (MBSE) and the synergy of MBSE with simulation technology and digital engineering. Contributors have submitted papers on MBSE methods, modeling approaches, integration of digital engineering with MBSE, standards, modeling languages, ontologies and metamodels, and economics analysis of MBSE to respond to the challenges posed by 21st century systems. What distinguishes this volume are the latest advances in MBSE research, the convergence of MBSE with digital engineering, and recent advances in applied research in MBSE, including growing convergence with systems science and decision science. This volume is appropriate as a reference text in graduate engineering courses in Model-Based Systems Engineering.