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 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 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.

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.

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.

This volume consists of 14 contributed chapters written by leading experts, offering in-depth discussions of the mathematical modeling and algorithmic aspects for tackling a range of space engineering applications. This book will be of interest to researchers and practitioners working in the field of space engineering. Since it offers an in-depth exposition of the mathematical modelling, algorithmic and numerical solution aspects of the topics covered, the book will also be useful to aerospace engineering graduates and post-graduate students who wish to expand their knowledge by studying real-world applications and challenges that they will encounter in their profession. Readers will obtain a broad overview of some of the most challenging space engineering operational scenarios of today and tomorrow: this will be useful for managers in the aerospace field, as well as in other industrial sectors. The contributed chapters are mainly focused on space engineering practice. Researchers and practitioners in mathematical systems modelling, operations research, optimization, and optimal control will also benefit from the case studies presented in this book. The model development and optimization approaches discussed can be extended towards other application areas that are not directly related to space engineering. Therefore, the book can be a useful reference to assist in the development of new modelling and optimization applications.

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 introduces several mathematical models in assembly line balancing based on stochastic programming and develops exact and heuristic methods to solve them. An assembly line system is a manufacturing process in which parts are added in sequence from workstation to workstation until the final assembly is produced. In an assembly line balancing problem, tasks belonging to different product models are allocated to workstations according to their processing times and precedence relationships among tasks. It incorporates two features, uncertain task times, and demand volatility, separately and simultaneously, into the conventional assembly line balancing model. A real-life case study related to the mask production during the COVID-19 pandemic is presented to illustrate the application of the proposed framework and methodology. The book is intended for graduate students who are interested in combinatorial optimizations in manufacturing with uncertain input.

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 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 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.

Volume IV of the series "Mathematics and Physics Applied to Science and Technology," this comprehensive six-book set covers: Linear Differential Equations and Oscillators Non-linear Differential Equations and Dynamical Systems Higher-order Differential Equations and Elasticity Simultaneous Systems of Differential Equations and Multi-dimensional Oscillators Singular Differential Equations and Special Functions Classification and Examples of Differential Equations and their Applications

The paradigms of dynamic games play an important role in the development of multi-agent models in engineering, economics, and management science. The applicability of their concepts stems from the ability to encompass situations with uncertainty, incomplete information, fluctuating coalition structure, and coupled constraints imposed on the strategies of all the players. This book - an outgrowth of the 10th International Symposium on Dynamic Games - presents current developments of the theory of dynamic games and its applications to various domains, in particular energy-environment economics and management sciences. The volume uses dynamic game models of various sorts to approach and solve several problems pertaining to pursuit-evasion, marketing, finance, climate and environmental economics, resource exploitation, as well as auditing and tax evasions. In addition, it includes some chapters on cooperative games, which are increasingly drawing dynamic approaches to their classical solutions. dynamic game theory and its applications for researchers, practitioners, and graduate students in applied mathematics, engineering, economics, as well as environmental and management sciences.

This text bridges the gulf between theoretical economic principles of negotiation and auction theory and their multifaceted applications in actual practice. It is intended to be a supplement to the already existing literature, as a comprehensive collection of reports detailing experiences and results of very different negotiations and auctions.

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

Provides well-written self-contained chapters, including problem sets and exercises, making it ideal for the classroom setting; Introduces applied optimization to the hazardous waste blending problem; Explores linear programming, nonlinear programming, discrete optimization, global optimization, optimization under uncertainty, multi-objective optimization, optimal control and stochastic optimal control; Includes an extensive bibliography at the end of each chapter and an index; GAMS files of case studies for Chapters 2, 3, 4, 5, and 7 are linked to http://www.springer.com/math/book/978-0-387-76634-8; Solutions manual available upon adoptions.

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.

This book describes a system of mathematical models and methods that can be used to analyze real economic and managerial decisions and to improve their effectiveness. Application areas include: management of development and operation budgets, assessment and management of economic systems using an energy entropy approach, equation of exchange rates and forecasting foreign exchange operations, evaluation of innovative projects, monitoring of governmental programs, risk management of investment processes, decisions on the allocation of resources, and identification of competitive industrial clusters. The proposed methods and models were tested on the example of Kazakhstan's economy, but the generated solutions will be useful for applications at other levels and in other countries. Regarding your book "Mathematical Methods and Models in Economics", I am impressed because now it is time when "econometrics" is becoming more appreciated by economists and by schools that are the hosts or employers of modern economists. ... Your presented results really impressed me. John F. Nash, Jr., Princeton University, Nobel Memorial Prize in Economic Sciences The book is within my scope of interest because of its novelty and practicality. First, there is a need for realistic modeling of complex systems, both natural and artificial that conclude computer and economic systems. There has been an ongoing effort in developing models dealing with complexity and incomplete knowledge. Consequently, it is clear to recognize the contribution of Mutanov to encapsulate economic modeling with emphasis on budgeting and innovation. Secondly, the method proposed by Mutanov has been verified by applying to the case of the Republic of Kazakhstan, with her vibrant emerging economy. Thirdly, Chapter 5 of the book is of particular interest for the computer technology community because it deals with innovation. In summary, the book of Mutanov should become one of the outstanding recognized pragmatic guides for dealing with innovative systems. Andrzej Rucinski, University of New Hampshire This book is unique in its theoretical findings and practical applicability. The book is an illuminating study based on an applied mathematical model which uses methods such as linear programming and input-output analysis. Moreover, this work demonstrates the author's great insight and academic brilliance in the fields of finance, technological innovations and marketing vis-a-vis the market economy. From both theoretical and practical standpoint, this work is indeed a great achievement. Yeon Cheon Oh, President of Seoul National University

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.

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.

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.

Herbert Scarf is a highly esteemed distinguished American economist. He is internationally famous for his early epoch-making work on optimal inventory policies and his highly influential study with Andrew Clark on optimal policies for a multi-echelon inventory problem, which initiated the important and flourishing field of supply chain management. Equally, he has gained world recognition for his classic study on the stability of the Walrasian price adjustment processes and his fundamental analysis on the relationship between the core and the set of competitive equilibria (the so-called Edgeworth conjecture). Further achievements include his remarkable sufficient condition for the existence of a core in non-transferable utility games and general exchange economies, his seminal paper with Lloyd Shapley on housing markets, and his pioneering study on increasing returns and models of production in the presence of indivisibilities. All in all, however, the name of Scarf is always remembered as a synonym for the computation of economic equilibria and fixed points. In the early 1960s he invented a path-breaking technique for computing equilibrium prices.This work has generated a major research field in economics termed Applied General Equilibrium Analysis and a corresponding area in operations research known as Simplicial Fixed Point Methods. This book comprises all his research articles and consists of four volumes. The volume collects Herbert Scarf's papers in the area of Applied Equilibrium Analysis.

Mathematica by Example, Sixth Edition is an essential resource for the Mathematica user, providing step-by-step instructions on achieving results from this powerful software tool. The book fully accounts for the changes to functionality and visualization capabilities and accomodates the full array of new extensions in the types of data and problems that Mathematica can immediately handle, including cloud services and systems, geographic and geometric computation, dynamic visualization, interactive applications and other improvements. It is an ideal text for scientific students, researchers, and aspiring programmers seeking further understanding of Mathematica. Written by seasoned practitioners with a view to practical implementation and problem-solving, the book's pedagogy is delivered clearly and without jargon using representative biological, physical and engineering problems. Code is provided on an ancillary website to support the use of Mathematica across diverse applications and subject areas.

This book contains state-of-the-art contributions in the field of evolutionary and deterministic methods for design, optimization and control in engineering and sciences. Specialists have written each of the 34 chapters as extended versions of selected papers presented at the International Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2013). The conference was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Topics treated in the various chapters are classified in the following sections: theoretical and numerical methods and tools for optimization (theoretical methods and tools; numerical methods and tools) and engineering design and societal applications (turbo machinery; structures, materials and civil engineering; aeronautics and astronautics; societal applications; electrical and electronics applications), focused particularly on intelligent systems for multidisciplinary design optimization (mdo) problems based on multi-hybridized software, adjoint-based and one-shot methods, uncertainty quantification and optimization, multidisciplinary design optimization, applications of game theory to industrial optimization problems, applications in structural and civil engineering optimum design and surrogate models based optimization methods in aerodynamic design.

This book outlines the latest trends in the use of multicriteria analysis in agriculture by highlighting recent applications for modeling agricultural decision-making. It introduces specific case studies using multicriteria analysis as a method for selecting multiattribute discrete alternatives or solving multiobjective planning problems. The book is intended for a broad readership, including agricultural and environmental economists, engineers and all scientists whose work involves the management of agricultural resources and decision-making in agriculture. The methods and applications presented in this book cover decision-making processes in agricultural and environmental contexts. The methodologies described consider multiple criteria simultaneously in a wide range of complex decision-making contexts by taking into account multiple, conflicting criteria. Given the wide range of case studies covered, the book offers a comprehensive guide to decision-making in the agricultural context and beyond.