Computing Equilibria and Fixed Points is devoted to the computation of equilibria, fixed points and stationary points. This volume is written with three goals in mind: (i) To give a comprehensive introduction to fixed point methods and to the definition and construction of Gr bner bases; (ii) To discuss several interesting applications of these methods in the fields of general equilibrium theory, game theory, mathematical programming, algebra and symbolic computation; (iii) To introduce several advanced fixed point and stationary point theorems. These methods and topics should be of interest not only to economists and game theorists concerned with the computation and existence of equilibrium outcomes in economic models and cooperative and non-cooperative games, but also to applied mathematicians, computer scientists and engineers dealing with models of highly nonlinear systems of equations (or polynomial equations).

This book provides a Management Science approach to quality management in food production. Aspects of food quality, product conformance and reliability/food safety are examined, starting with wheat and ending with its value chain transformation into bread. Protein qualities that influence glycemic index levels in bread are used to compare the value chains of France and the US. With Kaizen models the book shows how changes in these characteristics are the result of management decisions made by the wheat growers in response to government policy and industry strategy. Lately, it provides step-by-step instructions on how to apply kaizen methodology and Deming's work on quality improvement to make the HACCPs (Hazard Analysis and Critical Control Points) in food safety systems more robust.

This book presents a novel unified treatment of inverse problems in optimal control and noncooperative dynamic game theory. It provides readers with fundamental tools for the development of practical algorithms to solve inverse problems in control, robotics, biology, and economics. The treatment involves the application of Pontryagin's minimum principle to a variety of inverse problems and proposes algorithms founded on the elegance of dynamic optimization theory. There is a balanced emphasis between fundamental theoretical questions and practical matters. The text begins by providing an introduction and background to its topics. It then discusses discrete-time and continuous-time inverse optimal control. The focus moves on to differential and dynamic games and the book is completed by consideration of relevant applications. The algorithms and theoretical results developed in Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory provide new insights into information requirements for solving inverse problems, including the structure, quantity, and types of state and control data. These insights have significant practical consequences in the design of technologies seeking to exploit inverse techniques such as collaborative robots, driver-assistance technologies, and autonomous systems. The book will therefore be of interest to researchers, engineers, and postgraduate students in several disciplines within the area of control and robotics.

This book will serve as a reference, presenting state-of-the-art research on theoretical aspects of optimal sensor coverage problems. Readers will find it a useful tool for furthering developments on theory and applications of optimal coverage; much of the content can serve as material for advanced topics courses at the graduate level. The book is well versed with the hottest research topics such as Lifetime of Coverage, Weighted Sensor Cover, k-Coverage, Heterogeneous Sensors, Barrier, Sweep and Partial Coverage, Mobile Sensors, Camera Sensors and Energy-Harvesting Sensors, and more. Topics are introduced in a natural order from simple covers to connected covers, to the lifetime problem. Later, the book begins revisiting earlier problems ranging from the introduction of weights to coverage by k sensors and partial coverage, and from sensor heterogeneity to novel problems such as the barrier coverage problem. The book ends with coverage of mobile sensors, camera sensors, energy-harvesting sensors, underwater sensors, and crowdsensing.

The book begins with an introduction to software reliability, models and techniques. The book is an informative book covering the strategies needed to assess software failure behaviour and its quality, as well as the application of optimization tools for major managerial decisions related to the software development process. It features a broad range of topics including software reliability assessment and apportionment, optimal allocation and selection decisions and upgradations problems. It moves through a variety of problems related to the evolving field of optimization of software reliability engineering, including software release time, resource allocating, budget planning and warranty models, which are each explored in depth in dedicated chapters. This book provides a comprehensive insight into present-day practices in software reliability engineering, making it relevant to students, researchers, academics and practising consultants and engineers.

The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three parts: - Part I: A brief introduction to (Schwartz) distribution theory. Elements from the theories of ultra distributions and (Fourier) hyperfunctions are given in addition to some deeper results for Schwartz distributions, thus providing a rather comprehensive introduction to the theory of generalized functions. Basic properties and methods for distributions are developed with applications to constant coefficient ODEs and PDEs. The relation between distributions and holomorphic functions is considered, as well as basic properties of Sobolev spaces. - Part II: Fundamental facts about Hilbert spaces. The basic theory of linear (bounded and unbounded) operators in Hilbert spaces and special classes of linear operators - compact, Hilbert-Schmidt, trace class, and Schroedinger operators, as needed in quantum physics and quantum information theory - are explored. This section also contains a detailed spectral analysis of all major classes of linear operators, including completeness of generalized eigenfunctions, as well as of (completely) positive mappings, in particular quantum operations. - Part III: Direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators. The authors conclude with a discussion of the Hohenberg-Kohn variational principle. The appendices contain proofs of more general and deeper results, including completions, basic facts about metrizable Hausdorff locally convex topological vector spaces, Baire's fundamental results and their main consequences, and bilinear functionals. Mathematical Methods in Physics is aimed at a broad community of graduate students in mathematics, mathematical physics, quantum information theory, physics and engineering, as well as researchers in these disciplines. Expanded content and relevant updates will make this new edition a valuable resource for those working in these disciplines.

Today, the optimization of production planning processes by means of IT and quantitative methods is a de-facto standard in the energy industry. Franch et al. inChapter1andIkenouyeinChapter2giveanintroduction, overview, and reasonsforthis. Furthermore, theenergyproblemnowisnotonlyachallenging one but also one of the most important issues in the world from the political and economical points of view. In every country, the government is faced with the problem of how to adopt the system of 'Cap and Trade. ' Especially energy consuming industries, such as steel, power, oil and chemicals, are seriously confronted with this problem. VIII Preface This is also the reason why the German Operations Research Society (GOR) and one of its working groups, held a symposium with the title "Stochastic Optimization in the Energy Industry. " During the 78th meeting of the GOR working group "Praxis der Mathematischen Optimierung/Real World Optimization" in Aachen at Procom GmbH on April 21/22, 2007, the speakers with an application background explained their requirements for stochasticoptimizationsolutionsbasedonpracticalexperiences. Thespeakers from the research side and the software system suppliers examined di?erent aspects of the whole subject - from the integration of wind energy, the chain of errors in nuclear power plants and the scheduling of hydroelectric power stations, and the risk assessment in trading activities to the various software systems which support stochastic optimization methods. The symposium o?ered an interesting overview which re?ected the - quirements, possibilities and restrictions of "Stochastic Optimization in the Energy Industry.

During the 1980s, economic theory has been revolutionised by game theory. The game theory approach is now very widely used throughout the profession and has become a major tool for the construction of new economic models. It is the basic tool in the construction of a modern theory of industrial organisation and it has led to important developments in finance, labour economics and international trade. This major new collection - prepared by a leading international authority - is oriented towards researchers, professors and graduate students who are interested in the interface between game theory and economic theory. They include the seminal and most important recent papers on the development and application of game theory in economics.

Dynamic game theory serves the purpose of including strategic interaction in decision making and is therefore often applied to economic problems. This book presents the state-of-the-art and directions for future research in dynamic game theory related to economics. It was initiated by contributors to the 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics and combines a selection of papers from the workshop with invited papers of high quality.

This book covers some important topics in the construction of computable general equilibrium (CGE) models and examines use of these models for the analysis of economic policies, their properties, and their implications. Readers will find explanation and discussion of the theoretical structure and practical application of several model typologies, including dynamic, stochastic, micro-macro, and simulation models, as well as different closure rules and policy experiments. The presentation of applications to various country and problem-specific case studies serves to provide an informed and clearly articulated summary of the state of the art and the most important methodological advancements in the field of policy modeling within the framework of general equilibrium analysis. The book is an outcome of a recent workshop of the Italian Development Economists Association attended by a group of leading practitioners involved in the generation of CGE models and research on modeling the economy and policy making. It will be of interest to researchers, professional economists, graduate students, and knowledgeable policy makers.

This book features contributions from the GTM 2020 International Meeting on Game Theory held virtually from St. Petersburg, Russia, including presentations by plenary speakers. The topics cover a wide range of game-theoretic models and include both theory and applications, including applications to management.

This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.

Designs in nanoelectronics often lead to challenging simulation problems and include strong feedback couplings. Industry demands provisions for variability in order to guarantee quality and yield. It also requires the incorporation of higher abstraction levels to allow for system simulation in order to shorten the design cycles, while at the same time preserving accuracy. The methods developed here promote a methodology for circuit-and-system-level modelling and simulation based on best practice rules, which are used to deal with coupled electromagnetic field-circuit-heat problems, as well as coupled electro-thermal-stress problems that emerge in nanoelectronic designs. This book covers: (1) advanced monolithic/multirate/co-simulation techniques, which are combined with envelope/wavelet approaches to create efficient and robust simulation techniques for strongly coupled systems that exploit the different dynamics of sub-systems within multiphysics problems, and which allow designers to predict reliability and ageing; (2) new generalized techniques in Uncertainty Quantification (UQ) for coupled problems to include a variability capability such that robust design and optimization, worst case analysis, and yield estimation with tiny failure probabilities are possible (including large deviations like 6-sigma); (3) enhanced sparse, parametric Model Order Reduction techniques with a posteriori error estimation for coupled problems and for UQ to reduce the complexity of the sub-systems while ensuring that the operational and coupling parameters can still be varied and that the reduced models offer higher abstraction levels that can be efficiently simulated. All the new algorithms produced were implemented, transferred and tested by the EDA vendor MAGWEL. Validation was conducted on industrial designs provided by end-users from the semiconductor industry, who shared their feedback, contributed to the measurements, and supplied both material data and process data. In closing, a thorough comparison to measurements on real devices was made in order to demonstrate the algorithms' industrial applicability.

DYNAMIC OPTIMIZATION AND DIFFERENTIAL GAMES has been written to address the increasing number of Operations Research and Management Science problems (that is, applications) that involve the explicit consideration of time and of gaming among multiple agents. It is a book that will be used both as a textbook and as a reference and guide to engineers, operation researchers, applied mathematicians and social scientists whose work involves the theoretical aspects of dynamic optimization and differential games. Included throughout the text are detailed explanations of several original dynamic and game-theoretic mathematical models, which are of particular relevance in todaya (TM)s technologically-driven-global economy: revenue management, supply chain management, electric power systems, urban freight systems, dynamic congestion pricing, dynamic traffic assignment, electronic commerce and the Internet. In addition, there will be some more traditional applications with useful pedagogical content included in Chapter 1.

The book combines an emphasis on deterministic models and methods along with an introduction to stochastic optimal control and stochastic differential games. And most important, the book covers both theory and applications. It develops the key results of deterministic, continuous time, optimal control theory from both the classical calculus of variations perspectives and the more modern approach of infinite dimensional mathematical programming. Infinite dimensional mathematical programming provides greater utility for solving continuous-time-differential-game problems.

This book presents open optimization problems in graph theory and networks. Each chapter reflects developments in theory and applications based on Gregory Gutin's fundamental contributions to advanced methods and techniques in combinatorial optimization. Researchers, students, and engineers in computer science, big data, applied mathematics, operations research, algorithm design, artificial intelligence, software engineering, data analysis, industrial and systems engineering will benefit from the state-of-the-art results presented in modern graph theory and its applications to the design of efficient algorithms for optimization problems. Topics covered in this work include: * Algorithmic aspects of problems with disjoint cycles in graphs * Graphs where maximal cliques and stable sets intersect * The maximum independent set problem with special classes * A general technique for heuristic algorithms for optimization problems * The network design problem with cut constraints * Algorithms for computing the frustration index of a signed graph * A heuristic approach for studying the patrol problem on a graph * Minimum possible sum and product of the proper connection number * Structural and algorithmic results on branchings in digraphs * Improved upper bounds for Korkel--Ghosh benchmark SPLP instances

There is a widening gap between the current organizational reality and the tools and methods available to managers for addressing its challenges. Game Based Organization Design shows that one of the ways to bridge this gap is to introduce insights and approaches from video game design into the design of organizational systems. This book takes basic ideas such as games, play, and rules as the foundation for a new approach to organizational design and strategy formulation. Based on seven years of research and consulting work, this is the first time these original ideas have been made available in such a comprehensive and accessible manner to both executives and students of management. Game Based Organization Design combines a sound theoretical basis with many examples of practical application as well as useful pointers for readers who wish to put these ideas into action.

Nash equilibrium is the central solution concept in Game Theory. Since Nash's original paper in 1951, it has found countless applications in modeling strategic behavior of traders in markets, (human) drivers and (electronic) routers in congested networks, nations in nuclear disarmament negotiations, and more. A decade ago, the relevance of this solution concept was called into question by computer scientists, who proved (under appropriate complexity assumptions) that computing a Nash equilibrium is an intractable problem. And if centralized, specially designed algorithms cannot find Nash equilibria, why should we expect distributed, selfish agents to converge to one? The remaining hope was that at least approximate Nash equilibria can be efficiently computed.Understanding whether there is an efficient algorithm for approximate Nash equilibrium has been the central open problem in this field for the past decade. In this book, we provide strong evidence that even finding an approximate Nash equilibrium is intractable. We prove several intractability theorems for different settings (two-player games and many-player games) and models (computational complexity, query complexity, and communication complexity). In particular, our main result is that under a plausible and natural complexity assumption ("Exponential Time Hypothesis for PPAD"), there is no polynomial-time algorithm for finding an approximate Nash equilibrium in two-player games. The problem of approximate Nash equilibrium in a two-player game poses a unique technical challenge: it is a member of the class PPAD, which captures the complexity of several fundamental total problems, i.e., problems that always have a solution; and it also admits a quasipolynomial time algorithm. Either property alone is believed to place this problem far below NP-hard problems in the complexity hierarchy; having both simultaneously places it just above P, at what can be called the frontier of intractability. Indeed, the tools we develop in this book to advance on this frontier are useful for proving hardness of approximation of several other important problems whose complexity lies between P and NP: Brouwer's fixed point, market equilibrium, CourseMatch (A-CEEI), densest k-subgraph, community detection, VC dimension and Littlestone dimension, and signaling in zero-sum games.

Like norms, translation invariant functions are a natural and powerful tool for the separation of sets and scalarization. This book provides an extensive foundation for their application. It presents in a unified way new results as well as results which are scattered throughout the literature. The functions are defined on linear spaces and can be applied to nonconvex problems. Fundamental theorems for the function class are proved, with implications for arbitrary extended real-valued functions. The scope of applications is illustrated by chapters related to vector optimization, set-valued optimization, and optimization under uncertainty, by fundamental statements in nonlinear functional analysis and by examples from mathematical finance as well as from consumer and production theory. The book is written for students and researchers in mathematics and mathematical economics. Engineers and researchers from other disciplines can benefit from the applications, for example from scalarization methods for multiobjective optimization and optimal control problems.

Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today's state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book.

The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.

Global optimization aims at solving the most general problems of deterministic mathematical programming: to find the global optimum of a nonlinear, nonconvex, multivariate function of continuous and/or integer variables subject to constraints which may be themselves nonlinear and nonconvex. In addition, once the solutions are found, proof of its optimality is also expected from this methodology. Therefore, with these difficulties in mind, global optimization is becoming an increasingly powerful and important methodology. Essays and Surveys in Global Optimization is the most recent examination of its mathematical capability, power, and wide ranging solutions to many fields in the applied sciences.

This book focuses on the latest advances in nonlinear dynamic modeling in economics and finance, mainly-but not solely-based on the description of strategic interaction by using concepts and methods from dynamic and evolutionary game theory. The respective chapters cover a range of theoretical issues and examples concerning how the qualitative theory of dynamical systems is used to analyze the local and global bifurcations that characterize complex behaviors observed in social systems where heterogeneous and boundedly rational economic agents interact. Nonlinear dynamical systems, represented by difference and differential and functional equations, are extensively used to simulate the behavior of time-evolving economic systems, also in the presence of time lags, discontinuities, and hysteresis phenomena. In addition, some theoretical issues and particular applications are discussed, as well. The contributions gathered here offer an up-to-date review of the latest research in this rapidly developing research area.

This book presents the application of some AI related optimization techniques in the operation and control of electric power systems. With practical applications and examples the use of functional analysis, simulated annealing, Tabu-search, Genetic algorithms and fuzzy systems for the optimization of power systems is discussed in detail. Preliminary mathematical concepts are presented before moving to more advanced material. Researchers and graduate students will benefit from this book. Engineers working in utility companies, operations and control, and resource management will also find this book useful.

The aim of Cooperative Games on Combinatorial Structures is to analyze conflict situations in which two or more players can make coalitions and obtain prizes and penalties. This approach to situations of competition and cooperation was given in the seminal treatise by John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior. Cooperative game theory has succeeded in providing many applications of game theory. In this volume, games defined on combinatorial structures will be analyzed, i.e. a set system over a set of players. In many situations the author will work in a closure space. Examples of closure operators are the spanning operator of linear algebra and all convex hull operators. Chapters 1-4 constitute a review of mathematical concepts from Cooperative Game Theory, Graph Theory, Linear and Integer Programming, Combinatorial Optimization, Discrete Convex Analysis and Computational Complexity. The table of contents is a short guide to the topics and methods covered in this book. In Chapters 11 and 12, several notebooks are presented with the system Mathematica by Wolfram in the contexts of the packages DiscreteMath (Skiena) and Cooperative (Carter). There will also be found in the book several research projects. These are intended to offer new ideas that the reader should consider with caution. This book will be of interest to graduate students with some experience in game theory or mathematical programming and professional researchers in game theory, operational research and its applications in economic theory, and the political and social sciences. In addition, it will be especially useful for professionals who are interested in models for understanding and managing conflicts: management and operational research scientists, political and military scientists, and professional negotiators.