The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning.Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications.Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class.

This proceedings volume contains a selection of papers presented at the Fourth International Conference on High Performance Scientific Computing held at the Hanoi Institute of Mathematics, Vietnamese Academy of Science and Technology (VAST), March 2-6, 2009. The conference was organized by the Hanoi Institute of Mathematics, the Interdisciplinary Center for Scientific Computing (IWR), Heidelberg, and its Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences, and Ho Chi Minh City University of Technology. The contributions cover the broad interdisciplinary spectrum of scientific computing and present recent advances in theory, development of methods, and applications in practice. Subjects covered are mathematical modelling, numerical simulation, methods for optimization and control, parallel computing, software development, applications of scientific computing in physics, mechanics, biology and medicine, engineering, hydrology problems, transport, communication networks, production scheduling, industrial and commercial problems.

This book presents the latest researches on hypersonic steady glide dynamics and guidance, including the concept of steady glide reentry trajectory and the stability of its regular perturbation solutions, trajectory damping control technique for hypersonic glide reentry, singular perturbation guidance of hypersonic glide reentry, trajectory optimization based on steady glide, linear pseudospectral generalized nominal effort miss distance guidance, analytical entry guidance and trajectory-shaping guidance with final speed and load factor constraints. They can be used to solve many new difficult problems in entry guidance. And many practical engineering cases are provided for the readers for better understanding. Researchers and students in the fields of flight vehicle design or flight dynamics, guidance and control could use the book as valuable reference.

This book is one of the first to include an extensive discussion of integrated public transport planning. In times of growing urban populations and increasing environmental awareness, the importance of optimizing public transport systems is ever-developing. Three different aspects are presented: line planning, timetabling, and vehicle scheduling. Classically, challenges concerning these three aspects of planning are solved sequentially. Due to their high interdependence, the author presents a clear and detailed analysis of innovative, integrated models with accompanied numerical experiments performed to assess, and often support, the benefits of integration. The book will appeal to a wide readership ranging from graduate students to researchers.

The uneven geographical distribution of economic activities is a huge challenge worldwide and also for the European Union. In Krugman's New Economic Geography economic systems have a simple spatial structure. This book shows that more sophisticated models should visualise the EU as an evolving trade network with a specific topology and different aggregation levels. At the highest level, economic geography models give a bird eye's view of spatial dynamics. At a medium level, institutions shape the economy and the structure of (financial and labour) markets. At the lowest level, individual decisions interact with the economic, social and institutional environment; the focus is on firms' decision on location and innovation. Such multilevel models exhibit complex dynamic patterns - path dependence, cumulative causation, hysteresis - on a network structure; and specific analytic tools are necessary for studying strategic interaction, heterogeneity and nonlinearities.

General Fractional Derivatives with Applications in Viscoelasticity introduces the newly established fractional-order calculus operators involving singular and non-singular kernels with applications to fractional-order viscoelastic models from the calculus operator viewpoint. Fractional calculus and its applications have gained considerable popularity and importance because of their applicability to many seemingly diverse and widespread fields in science and engineering. Many operations in physics and engineering can be defined accurately by using fractional derivatives to model complex phenomena. Viscoelasticity is chief among them, as the general fractional calculus approach to viscoelasticity has evolved as an empirical method of describing the properties of viscoelastic materials. General Fractional Derivatives with Applications in Viscoelasticity makes a concise presentation of general fractional calculus.

The roles and applications of various modeling approaches, aimed at improving the usefulness of energy policy models in public decision making, are covered by this book. The development, validation, and applications of system dynamics and agent-based models in service of energy policy design and assessment in the 21st century is a key focus. A number of modeling approaches and models for energy policy, with a particular focus on low-carbon economic development of regions and states are covered. Chapters on system dynamics methodology, model-based theory, fuzzy system dynamics frame-work, and optimization modeling approach are presented, along with several chapters on future research opportunities for the energy policy modeling community. The use of model-based analysis and scenarios in energy policy design and assessment has seen phenomenal growth during the past several decades. In recent years, renewed concerns about climate change and energy security have posed unique modeling challenges. By utilizing the validation techniques and procedures which are effectively demonstrated in these contributions, researchers and practitioners in energy systems domain can increase the appeal and acceptance of their policy models.

This book provides a comprehensive overview of the most important and frequently considered optimization problems concerning cutting and packing. Based on appropriate modeling approaches for the problems considered, it offers an introduction to the related solution methods. It also addresses aspects like performance results for heuristic algorithms and bounds of the optimal value, as well as the packability of a given set of objects within a predefined container. The problems discussed arise in a wide variety of different fields of application and research, and as such, the fundamental knowledge presented in this book make it a valuable resource for students, practitioners, and researchers who are interested in dealing with such tasks.

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.

The book titled "Optimization Techniques" is based on optimization techniques and O.R. related courses for undergraduate and postgraduate engineering and mathematics students of various universities as well as for researchers working on optimization problems. The main objective of the book is to acquaint and familiarize the readers with different types of optimization techniques, solving optimization problems, implementing computational techniques, abstracting mathematical results and proofs etc. The book gives a clear appreciation and good grasp over most of the currently available optimization techniques. Each method developed has been illustrated with solved examples. A set of exercises for self practice is given at the end of each chapter. A set of brief answer review questions relating to the finer detail of the topics discussed in each chapter preceding the set of exercises has been added to facilitate learning and enhance the value of the book.

Cooperative Control of Multi-Agent Systems: An Optimal and Robust Perspective reports and encourages technology transfer in the field of cooperative control of multi-agent systems. The book deals with UGVs, UAVs, UUVs and spacecraft, and more. It presents an extended exposition of the authors' recent work on all aspects of multi-agent technology. Modelling and cooperative control of multi-agent systems are topics of great interest, across both academia (research and education) and industry (for real applications and end-users). Graduate students and researchers from a wide spectrum of specialties in electrical, mechanical or aerospace engineering fields will use this book as a key resource.

Providing readers with a detailed examination of resilient controls in risk-averse decision, this monograph is aimed toward researchers and graduate students in applied mathematics and electrical engineering with a systems-theoretic concentration. This work contains a timely and responsive evaluation of reforms on the use of asymmetry or skewness pertaining to the restrictive family of quadratic costs that have been appeared in various scholarly forums. Additionally, the book includes a discussion of the current and ongoing efforts in the usage of risk, dynamic game decision optimization and disturbance mitigation techniques with output feedback measurements tailored toward the worst-case scenarios. This work encompasses some of the current changes across uncertainty quantification, stochastic control communities, and the creative efforts that are being made to increase the understanding of resilient controls. Specific considerations are made in this book for the application of decision theory to resilient controls of the linear-quadratic class of stochastic dynamical systems. Each of these topics are examined explicitly in several chapters. This monograph also puts forward initiatives to reform both control decisions with risk consequences and correct-by-design paradigms for performance reliability associated with the class of stochastic linear dynamical systems with integral quadratic costs and subject to network delays, control and communication constraints.

The sequential quadratic hamiltonian (SQH) method is a novel numerical optimization procedure for solving optimal control problems governed by differential models. It is based on the characterisation of optimal controls in the framework of the Pontryagin maximum principle (PMP). The SQH method is a powerful computational methodology that is capable of development in many directions. The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems discusses its analysis and use in solving nonsmooth ODE control problems, relaxed ODE control problems, stochastic control problems, mixed-integer control problems, PDE control problems, inverse PDE problems, differential Nash game problems, and problems related to residual neural networks. This book may serve as a textbook for undergraduate and graduate students, and as an introduction for researchers in sciences and engineering who intend to further develop the SQH method or wish to use it as a numerical tool for solving challenging optimal control problems and for investigating the Pontryagin maximum principle on new optimisation problems. Feature Provides insight into mathematical and computational issues concerning optimal control problems, while discussing many differential models of interest in different disciplines. Suitable for undergraduate and graduate students and as an introduction for researchers in sciences and engineering. Accompanied by codes which allow the reader to apply the SQH method to solve many different optimal control and optimisation problems

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 book is devoted to the study of classes of optimal control problems arising in economic growth theory, related to the Robinson-Solow-Srinivasan (RSS) model. The model was introduced in the 1960s by economists Joan Robinson, Robert Solow, and Thirukodikaval Nilakanta Srinivasan and was further studied by Robinson, Nobuo Okishio, and Joseph Stiglitz. Since then, the study of the RSS model has become an important element of economic dynamics. In this book, two large general classes of optimal control problems, both of them containing the RSS model as a particular case, are presented for study. For these two classes, a turnpike theory is developed and the existence of solutions to the corresponding infinite horizon optimal control problems is established. The book contains 9 chapters. Chapter 1 discusses turnpike properties for some optimal control problems that are known in the literature, including problems corresponding to the RSS model. The first class of optimal control problems is studied in Chaps. 2-6. In Chap. 2, infinite horizon optimal control problems with nonautonomous optimality criteria are considered. The utility functions, which determine the optimality criterion, are nonconcave. This class of models contains the RSS model as a particular case. The stability of the turnpike phenomenon of the one-dimensional nonautonomous concave RSS model is analyzed in Chap. 3. The following chapter takes up the study of a class of autonomous nonconcave optimal control problems, a subclass of problems considered in Chap. 2. The equivalence of the turnpike property and the asymptotic turnpike property, as well as the stability of the turnpike phenomenon, is established. Turnpike conditions and the stability of the turnpike phenomenon for nonautonomous problems are examined in Chap. 5, with Chap. 6 devoted to the study of the turnpike properties for the one-dimensional nonautonomous nonconcave RSS model. The utility functions, which determine the optimality criterion, are nonconcave. The class of RSS models is identified with a complete metric space of utility functions. Using the Baire category approach, the turnpike phenomenon is shown to hold for most of the models. Chapter 7 begins the study of the second large class of autonomous optimal control problems, and turnpike conditions are established. The stability of the turnpike phenomenon for this class of problems is investigated further in Chaps. 8 and 9.

This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.

Presenting a strong and clear relationship between theory and practice, Linear and Integer Optimization: Theory and Practice is divided into two main parts. The first covers the theory of linear and integer optimization, including both basic and advanced topics. Dantzig's simplex algorithm, duality, sensitivity analysis, integer optimization models, and network models are introduced. More advanced topics also are presented including interior point algorithms, the branch-and-bound algorithm, cutting planes, complexity, standard combinatorial optimization models, the assignment problem, minimum cost flow, and the maximum flow/minimum cut theorem. The second part applies theory through real-world case studies. The authors discuss advanced techniques such as column generation, multiobjective optimization, dynamic optimization, machine learning (support vector machines), combinatorial optimization, approximation algorithms, and game theory. Besides the fresh new layout and completely redesigned figures, this new edition incorporates modern examples and applications of linear optimization. The book now includes computer code in the form of models in the GNU Mathematical Programming Language (GMPL). The models and corresponding data files are available for download and can be readily solved using the provided online solver. This new edition also contains appendices covering mathematical proofs, linear algebra, graph theory, convexity, and nonlinear optimization. All chapters contain extensive examples and exercises. This textbook is ideal for courses for advanced undergraduate and graduate students in various fields including mathematics, computer science, industrial engineering, operations research, and management science.

Durable strategies that have prolonged effects are prevalent in real-world situations. Revenue-generating investments, toxic waste disposal, long-lived goods, regulatory measures, coalition agreements, diffusion of knowledge, advertisement and investments to accumulate physical capital are concrete and common examples of durable strategies. This book provides an augmentation of dynamic game theory and advances a new game paradigm with durable strategies in decision-making schemes. It covers theories, solution techniques, and the applications of a general class of dynamic games with multiple durable strategies. Non-cooperative equilibria and cooperative solutions are derived, along with advanced topics including random termination, asynchronous game horizons, and stochastic analysis. The techniques presented here will enable readers to solve numerous practical dynamic interactive problems with durable strategies. This book not only expands the scope of applied dynamic game theory, but also provides a solid foundation for further theoretical and technical advancements. As such, it will appeal to scholars and students of quantitative economics, game theory, operations research, and computational mathematics. "Not too many new concepts have been introduced in dynamic games since their inception. The introduction of the concept of durable strategies changes this trend and yields important contributions to environmental and business applications." Dusan M Stipanovic, Professor, University of Illinois at Urbana-Champaign "Before this book, the field simply did not realize that most of our strategies are durable and entail profound effects in the future. Putting them into the mathematical framework of dynamic games is a great innovative effort." Vladimir Turetsky, Professor, Ort Braude College "Durable-strategies Dynamic Games is truly a world-leading addition to the field of dynamic games. It is a much needed publication to tackle increasingly crucial problems under the reality of durable strategies." Vladimir Mazalov, Director of Mathematical Research, Russian Academy of Sciences & President of the International Society of Dynamic Games

Social Networks and Trust discusses two possible explanations for the emergence of trust via social networks. If network members can sanction untrustworthiness of actors, these actors may refrain from acting in an untrustworthy manner. Moreover, if actors are informed regularly about trustworthy behavior of others, trust will grow among these actors.
A unique combination of formal model building and empirical methodology is used to derive and test hypotheses about the effects of networks on trust. The models combine elements from game theory, which is mainly used in economics, and social network analysis, which is mainly used in sociology.
The hypotheses are tested (1) by analyzing contracts in information technology transactions from a survey on small and medium-sized enterprises and (2) by studying judgments of subjects in a vignette experiment related to hypothetical transactions with a used-car dealer.

The theory of dynamic games is very rich in nature and very much alive If the reader does not already agree with this statement, I hope he/she will surely do so after having consulted the contents of the current volume. The activities which fall under the heading of 'dynamic games' cannot easily be put into one scientific discipline. On the theoretical side one deals with differential games, difference games (the underlying models are described by differential, respec tively difference equations) and games based on Markov chains, with determin istic and stochastic games, zero-sum and nonzero-sum games, two-player and many-player games - all under various forms of equilibria. On the practical side, one sees applications to economics (stimulated by the recent Nobel prize for economics which went to three prominent scientists in game theory), biology, management science, and engineering. The contents of this volume are primarily based on selected presentations made at the Sixth International Symposium on Dynamic Games and Applica tions, held in St Jovite, Quebec, Canada, 13-15 July 1994. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival technical journals. This conference, as well as its predecessor which was held in Grimentz, 1992, took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. One of the activities of the ISDG is the publication of these Annals. The contributions in this volume have been grouped around five themes."

This book demonstrates what kind of problems, originating in a management accounting setting, may be solved with game theoretic models. Game theory has experienced growing interest and numerous applications in the field of management accounting. The main focus traditionally has been on the field of non-cooperative behaviour, but the area of cooperative game theory has developed rapidly and has received increasing attention. Intensive research, in combination with the changing culture of publishing, has produced a nearly unmanageable number of publications in the areas concerned. Therefore, one main purpose of this volume is providing an intensive analysis of the intersection of these areas. In addition, the book strengthens the relationship between the theory and the practical applications and it illustrates the two-sided relationship between game theory and management accounting: new game theoretic models offer new fields of applications and these applications raise new questions for the theory.

Mathematical methods and theories with interdisciplinary applications are presented in this book. The eighteen contributions presented in this Work have been written by eminent scientists; a few papers are based on talks which took place at the International Conference at the Hellenic Artillery School in May 2015. Each paper evaluates possible solutions to long-standing problems such as the solvability of the direct electromagnetic scattering problem, geometric approaches to cyber security, ellipsoid targeting with overlap, non-equilibrium solutions of dynamic networks, measuring ballistic dispersion, elliptic regularity theory for the numerical solution of variational problems, approximation theory for polynomials on the real line and the unit circle, complementarity and variational inequalities in electronics, new two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization, and strong and weak convexity of closed sets in a Hilbert space. Graduate students, scientists, engineers and researchers in pure and applied mathematical sciences, operations research, engineering, and cyber security will find the interdisciplinary scientific perspectives useful to their overall understanding and further research.

This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers' understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.

An innovative feature of this book is its econocentric structure, focusing on digital designs. From the outset, econocentrism is assumed to be a core engine of capitalism, like money. The new coronavirus pandemic has changed lifestyles worldwide, which are unlikely ever to return in their original form. This great transformation will change the nature of the socio-economic system itself and will be centered on digital designs. At present, money already is beginning to undergo a major revolution in that sense. Many books dealing with digital designs and innovations have been published, but few if any of them focus on monetary and analytical methods in the way that this present volume does.The book then contains 6 parts: Evolution of money and thinking complexities in the AI era; Goods market and the future of labor market; Computational social approaches to social dilemmas, smart city, cryptocurrencies; Artificial market experiments; The randomness and high frequencies in financial data; Other trading strategy issues and the effects of AI usage. These issues may be indispensable subjects in our age. Study these subject, and have a step forward to the future society!

This book includes selected peer-reviewed papers presented at the International Conference on Modeling, Simulation and Optimization (CoMSO 2021), organized by National Institute of Technology, Silchar, Assam, India, during December 16-18, 2021. The book covers topics of modeling, simulation and optimization, including computational modeling and simulation, system modeling and simulation, device/VLSI modeling and simulation, control theory and applications, modeling and simulation of energy systems and optimization. The book disseminates various models of diverse systems and includes solutions of emerging challenges of diverse scientific fields.