The goal of this book is to elaborate on the main principles of the theory of the Berge equilibrium by answering the following two questions: What are the basic properties of the Berge equilibrium? Does the Berge equilibrium exist, and how can it be calculated? The Golden Rule of ethics, which appears in Christianity, Judaism, Islam, Buddhism, Confucianism and other world religions, states the following: "Behave towards others as you would like them to behave towards you." In any game, each party of conflict seeks to maximize some payoff. Therefore, for each player, the Golden Rule is implemented through the maximization of his/her payoff by all other players, which matches well with the concept of the Berge equilibrium. The approach presented here will be of particular interest to researchers (including undergraduates and graduates) and economists focused on decision-making under complex conflict conditions. The peaceful resolution of conflicts is the cornerstone of the approach: as a matter of fact, the Golden Rule precludes military clashes and violence. In turn, the new approach requires new methods; in particular, the existence problems are reduced to saddle point design for the Germeier convolution of payoff functions, with further transition to mixed strategies in accordance with the standard procedure employed by E. Borel, J. von Neumann, J. Nash, and their followers. Moreover, this new approach has proven to be efficient and fruitful with regard to a range of other important problems in mathematical game theory, which are considered in the Appendix.

Traditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example tic-tac-toe, solitaire and hex. This is the subject of combinatorial game theory. Most board games are a challenge for mathematics: to analyze a position one has to examine the available options, and then the further options available after selecting any option, and so on. This leads to combinatorial chaos, where brute force study is impractical. In this comprehensive volume, Jozsef Beck shows readers how to escape from the combinatorial chaos via the fake probabilistic method, a game-theoretic adaptation of the probabilistic method in combinatorics. Using this, the author is able to determine exact results about infinite classes of many games, leading to the discovery of some striking new duality principles.

The Gradient Test: Another Likelihood-Based Test presents the latest on the gradient test, a large-sample test that was introduced in statistics literature by George R. Terrell in 2002. The test has been studied by several authors, is simply computed, and can be an interesting alternative to the classical large-sample tests, namely, the likelihood ratio (LR), Wald (W), and Rao score (S) tests. Due to the large literature about the LR, W and S tests, the gradient test is not frequently used to test hypothesis. The book covers topics on the local power of the gradient test, the Bartlett-corrected gradient statistic, the gradient statistic under model misspecification, and the robust gradient-type bounded-influence test.

This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics.

Many systems architecture optimization problems are characterized by a variable number of optimization variables. Many classical optimization algorithms are not suitable for such problems. The book presents recently developed optimization concepts that are designed to solve such problems. These new concepts are implemented using genetic algorithms and differential evolution. The examples and applications presented show the effectiveness of the use of these new algorithms in optimizing systems architectures. The book focuses on systems architecture optimization. It covers new algorithms and its applications, besides reviewing fundamental mathematical concepts and classical optimization methods. It also provides detailed modeling of sample engineering problems. The book is suitable for graduate engineering students and engineers. The second part of the book includes numerical examples on classical optimization algorithms, which are useful for undergraduate engineering students. While focusing on the algorithms and their implementation, the applications in this book cover the space trajectory optimization problem, the optimization of earth orbiting satellites orbits, and the optimization of the wave energy converter dynamic system: architecture and control. These applications are illustrated in the starting of the book, and are used as case studies in later chapters for the optimization methods presented in the book.

Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

This book contains selected papers presented at ICGEC 2021, the 14th International Conference on Genetic and Evolutionary Computing, held from October 21-23, 2021 in Jilin City, China. The conference was technically co-sponsored by Springer, Northeast Electric Power University Fujian University of Technology, Shandong University of Science and Technology, and Western Norway University of Applied Sciences. It is intended as an international forum for the researchers and professionals in all areas of genetic and evolutionary computing. And the readers may learn the up-to-date techniques of the mentioned topics, including swarm intelligence, artificial intelligence, information hiding and data mining techniques, which can help them to bring new ideas or apply the designed approaches from the collected papers to their professional jobs.

A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is thus an opportunity for popularizing these techniques among researchers involved in other sciences, including users of optimization in a wide sense, in mechanics, physics, statistics, finance and economics. Of use to research professionals, including graduate students at an advanced level.

The book focuses on Social Collective Intelligence, a term used to denote a class of socio-technical systems that combine, in a coordinated way, the strengths of humans, machines and collectives in terms of competences, knowledge and problem solving capabilities with the communication, computing and storage capabilities of advanced ICT. Social Collective Intelligence opens a number of challenges for researchers in both computer science and social sciences; at the same time it provides an innovative approach to solve challenges in diverse application domains, ranging from health to education and organization of work. The book will provide a cohesive and holistic treatment of Social Collective Intelligence, including challenges emerging in various disciplines (computer science, sociology, ethics) and opportunities for innovating in various application areas. By going through the book the reader will gauge insight and knowledge into the challenges and opportunities provided by this new, exciting, field of investigation. Benefits for scientists will be in terms of accessing a comprehensive treatment of the open research challenges in a multidisciplinary perspective. Benefits for practitioners and applied researchers will be in terms of access to novel approaches to tackle relevant problems in their field. Benefits for policy-makers and public bodies representatives will be in terms of understanding how technological advances can support them in supporting the progress of society and economy.

This book describes the fundamental and theoretical concepts of optimization algorithms in a systematic manner, along with their potential applications and implementation strategies in mining engineering. It explains basics of systems engineering, linear programming, and integer linear programming, transportation and assignment algorithms, network analysis, dynamic programming, queuing theory and their applications to mine systems. Reliability analysis of mine systems, inventory management in mines, and applications of non-linear optimization in mines are discussed as well. All the optimization algorithms are explained with suitable examples and numerical problems in each of the chapters. Features include: * Integrates operations research, reliability, and novel computerized technologies in single volume, with a modern vision of continuous improvement of mining systems. * Systematically reviews optimization methods and algorithms applied to mining systems including reliability analysis. * Gives out software-based solutions such as MATLAB (R), AMPL, LINDO for the optimization problems. * All discussed algorithms are supported by examples in each chapter. * Includes case studies for performance improvement of the mine systems. This book is aimed primarily at professionals, graduate students, and researchers in mining engineering.

Reviews the literature of the Moth-Flame Optimization algorithm; Provides an in-depth analysis of equations, mathematical models, and mechanisms of the Moth-Flame Optimization algorithm; Proposes different variants of the Moth-Flame Optimization algorithm to solve binary, multi-objective, noisy, dynamic, and combinatorial optimization problems; Demonstrates how to design, develop, and test different hybrids of Moth-Flame Optimization algorithm; Introduces several applications areas of the Moth-Flame Optimization algorithm focusing in sustainability.

This book presents new techniques and methods for distributed control and optimization of networked microgrids. Distributed consensus issues under network-based and event-triggered mechanisms are first addressed in a multi-agent system framework, which can explicitly characterize the relationship between communication resources and the control performance. Then, considering the effects of network uncertainties, multi-agent system-based distributed schemes are tailored to solve the fundamental issues of networked microgrids such as distributed frequency regulation, voltage regulation, active power sharing/load sharing, and energy management. The monograph will contribute to stimulating extensive interest of researchers in electrical and control fields.

This book reports on the latest advances in adaptive critic control with robust stabilization for uncertain nonlinear systems. Covering the core theory, novel methods, and a number of typical industrial applications related to the robust adaptive critic control field, it develops a comprehensive framework of robust adaptive strategies, including theoretical analysis, algorithm design, simulation verification, and experimental results. As such, it is of interest to university researchers, graduate students, and engineers in the fields of automation, computer science, and electrical engineering wishing to learn about the fundamental principles, methods, algorithms, and applications in the field of robust adaptive critic control. In addition, it promotes the development of robust adaptive critic control approaches, and the construction of higher-level intelligent systems.

This book presents the construction and resolution of 50 practical optimization problems and covers an exceptionally wide range, including games-associated problems (Unblock Me, Sudokus), logistical problems, and problems concerning plant distribution, production, operations scheduling, management and resource allocation. The problems are divided into 5 difficulty levels. Problems in the first few levels are focused on learning the model construction methodology, while those in the last level include complex optimization environments. For each problem solution, the specific steps are illustrated, promoting reader comprehension. In addition, all the models are implemented in an optimization library, LINGO, their solutions have been analyzed and their correct construction has been verified. The book also includes a simple guide to implementing models in LINGO in a straightforward manner and in any input data format (text files, spreadsheets or databases). As an ideal companion to the author's previously published work Modelling in Mathematical Programming, the book is intended as a basic tool for students of operations research, and for researchers in any advanced area involving mathematical programming.

Optimization plays an invaluable role in the exciting and rapidly developing field of computer vision, yet this importance is often overlooked in the literature.

This practical and authoritative text/reference presents a broad introduction to the optimization methods used specifically in computer vision. In order to facilitate understanding, the presentation of the methods is supplemented by simple flow charts, followed by pseudocode implementations that reveal deeper insights into their mode of operation. These discussions are further supported by examples taken from important applications in computer vision.

Topics and features: provides a comprehensive overview of computer vision-related optimization; covers a range of techniques from classical iterative multidimensional optimization to cutting-edge topics of graph cuts and GPU-suited total variation-based optimization; describes in detail the optimization methods employed in computer vision applications; illuminates key concepts with clearly written and step-by-step explanations; presents detailed information on implementation, including pseudocode for most methods.

This easy-to-follow and applications-focused book is an essential resource for researchers and practitioners seeking guidance on implementing specific methods in computer vision.

This book discusses an important area of numerical optimization, called interior-point method. This topic has been popular since the 1980s when people gradually realized that all simplex algorithms were not convergent in polynomial time and many interior-point algorithms could be proved to converge in polynomial time. However, for a long time, there was a noticeable gap between theoretical polynomial bounds of the interior-point algorithms and efficiency of these algorithms. Strategies that were important to the computational efficiency became barriers in the proof of good polynomial bounds. The more the strategies were used in algorithms, the worse the polynomial bounds became. To further exacerbate the problem, Mehrotra's predictor-corrector (MPC) algorithm (the most popular and efficient interior-point algorithm until recently) uses all good strategies and fails to prove the convergence. Therefore, MPC does not have polynomiality, a critical issue with the simplex method. This book discusses recent developments that resolves the dilemma. It has three major parts. The first, including Chapters 1, 2, 3, and 4, presents some of the most important algorithms during the development of the interior-point method around the 1990s, most of them are widely known. The main purpose of this part is to explain the dilemma described above by analyzing these algorithms' polynomial bounds and summarizing the computational experience associated with them. The second part, including Chapters 5, 6, 7, and 8, describes how to solve the dilemma step-by-step using arc-search techniques. At the end of this part, a very efficient algorithm with the lowest polynomial bound is presented. The last part, including Chapters 9, 10, 11, and 12, extends arc-search techniques to some more general problems, such as convex quadratic programming, linear complementarity problem, and semi-definite programming.

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.

With annual gross sales surpassing 100 billion U.S. dollars each of the last two years, the digital games industry may one day challenge theatrical-release movies as the highest-grossing entertainment media in the world. In their examination of the tremendous cultural influence of digital games, Daniel Reardon and David Wright analyze three companies that have shaped the industry: Bethesda, located in Rockville, Maryland, USA; BioWare in Edmonton, Alberta, Canada; and CD Projekt Red in Warsaw, Poland. Each company has used social media and technical content in the games to promote players' belief that players control the companies' game narratives. The result has been at times explosive, as empowered players often attempted to co-op the creative processes of games through discussion board forum demands, fund-raising campaigns to persuade companies to change or add game content, and modifications ("modding") of the games through fan-created downloads. The result has changed the way we understand the interactive nature of digital games and the power of fan culture to shape those games.

This book details cutting-edge research into human-like driving technology, utilising game theory to better suit a human and machine hybrid driving environment. Covering feature identification and modelling of human driving behaviours, the book explains how to design an algorithm for decision making and control of autonomous vehicles in complex scenarios. Beginning with a review of current research in the field, the book uses this as a springboard from which to present a new theory of human-like driving framework for autonomous vehicles. Chapters cover system models of decision making and control, driving safety, riding comfort and travel efficiency. Throughout the book, game theory is applied to human-like decision making, enabling the autonomous vehicle and the human driver interaction to be modelled using noncooperative game theory approach. It also uses game theory to model collaborative decision making between connected autonomous vehicles. This framework enables human-like decision making and control of autonomous vehicles, which leads to safer and more efficient driving in complicated traffic scenarios. The book will be of interest to students and professionals alike, in the field of automotive engineering, computer engineering and control engineering.

This book is about optimization techniques and is subdivided into two parts. In the first part a wide overview on optimization theory is presented. Optimization is presented as being composed of five topics, namely: design of experiment, response surface modeling, deterministic optimization, stochastic optimization, and robust engineering design. Each chapter, after presenting the main techniques for each part, draws application oriented conclusions including didactic examples. In the second part some applications are presented to guide the reader through the process of setting up a few optimization exercises, analyzing critically the choices which are made step by step, and showing how the different topics that constitute the optimization theory can be used jointly in an optimization process. The applications which are presented are mainly in the field of thermodynamics and fluid dynamics due to the author's background.

Very little has been published on optimization of pharmaceutical portfolios. Moreover, most of published literature is coming from the commercial side, where probability of technical success (PoS) is treated as fixed, and not as a consequence of development strategy or design. In this book there is a strong focus on impact of study design on PoS and ultimately on the value of portfolio. Design options that are discussed in different chapters are dose-selection strategies, adaptive design and enrichment. Some development strategies that are discussed are indication sequencing, optimal number of programs and optimal decision criteria. This book includes chapters written by authors with very broad backgrounds including financial, clinical, statistical, decision sciences, commercial and regulatory. Many authors have long held executive positions and have been involved with decision making at a product or at a portfolio level. As such, it is expected that this book will attract a very broad audience, including decision makers in pharmaceutical R&D, commercial and financial departments. The intended audience also includes portfolio planners and managers, statisticians, decision scientists and clinicians. Early chapters describe approaches to portfolio optimization from big Pharma and Venture Capital standpoints. They have stronger focus on finances and processes. Later chapters present selected statistical and decision analysis methods for optimizing drug development programs and portfolios. Some methodological chapters are technical; however, with a few exceptions they require a relatively basic knowledge of statistics by a reader.

This book covers using R for doing optimization, a key area of operations research, which has been applied to virtually every industry. The focus is on linear and mixed integer optimization. It uses an algebraic modeling approach for creating formulations that pairs naturally with an algebraic implementation in R. With the rapid rise of interest in data analytics, a data analytics platform is key. Working technology and business professionals need an awareness of the tools and language of data analysis. R reduces the barrier to entry for people to start using data analytics tools. Philosophically, the book emphasizes creating formulations before going into implementation. Algebraic representation allows for clear understanding and generalization of large applications, and writing formulations is necessary to explain and convey the modeling decisions made. Appendix A introduces R. Mathematics is used at the level of subscripts and summations Refreshers are provided in Appendix B. This book: * Provides and explains code so examples are relatively clear and self-contained. * Emphasizes creating algebraic formulations before implementing. * Focuses on application rather than algorithmic details. * Embodies the philosophy of reproducible research. * Uses open-source tools to ensure access to powerful optimization tools. * Promotes open-source: all materials are available on the author's github repository. * Demonstrates common debugging practices with a troubleshooting emphasis specific to optimization modeling using R. * Provides code readers can adapt to their own applications . This book can be used for graduate and undergraduate courses for students without a background in optimization and with varying mathematical backgrounds.

This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems. In the current interdisciplinary supercomputer-oriented research environment, semi-infinite fractional programming is among the most rapidly expanding research areas in terms of its multi-facet applications empowerment for real-world problems, which may stem from many control problems in robotics, outer approximation in geometry, and portfolio problems in economics, that can be transformed into semi-infinite problems as well as handled by transforming them into semi-infinite fractional programming problems. As a matter of fact, in mathematical optimisation programs, a fractional programming (or program) is a generalisation to linear fractional programming. These problems lay the theoretical foundation that enables us to fully investigate the second-order optimality and duality aspects of our principal fractional programming problem as well as its semi-infinite counterpart.

This book provides an enduring response to modern economic problems and the consequent crises, dealing with the economic modelling of nations and the forecasting of economic growth. The main arguments embodied constitute the creation of jobs and the restoration of economic growth, using the implicit acceptance of analysis on differential models and neutral systems for controlling the wealth of nations.