This Palgrave Pivot presents tournament design mainly within the axioms of incentive compatibility and fairness. It illustrates the advantages of an axiomatic approach through various examples, including several FIFA and UEFA tournaments, and uses theoretical tools and simulation methodology in its analysis. Chapter 1 discusses scoring systems of championships with multiple competitions, ranking in Swiss-system tournaments, and tie-breaking rules in round-robin leagues. It is followed by a thorough critical analysis of the current and previous FIFA World Rankings. The broad focus is substantially narrowed in Chapter 2, which turns to the topic of incentive (in)compatibility in multiple qualifiers. It is revealed that UEFA has faced at least three times recently this problem in the qualification to the UEFA Europa League, qualification to the UEFA Champions League, and the draw of the UEFA Champions League groups. Analogously, Chapter 3 discusses incentive (in)compatibility when there is only one group-based tournament but the complex progression rules to the subsequent stage can be designed poorly. Our examples include the qualifying tournaments of recent FIFA World Cups and UEFA European Championships. Chapter 4 moves to the problem of penalty shootout rules in soccer, where the fairness and complexity of some alternative mechanisms from the literature are evaluated. Fairness remains the central issue in Chapter 5, which presents the challenges of designing a tournament with 24 teams if the number of teams per group cannot exceed four. As expected, there is no perfect solution, and both FIFA and UEFA have introduced a reform in this format recently. Chapter 6 deals with the qualification for the 2020 UEFA European Football Championship. Its tournament design is perhaps the most complicated one that has ever been implemented in the real-world and suffers from serious shortcomings.

The rich, multi-faceted and multi-disciplinary field of matching-based market design is an active and important one due to its highly successful applications with economic and sociological impact. Its home is economics, but with intimate connections to algorithm design and operations research. With chapters contributed by over fifty top researchers from all three disciplines, this volume is unique in its breadth and depth, while still being a cohesive and unified picture of the field, suitable for the uninitiated as well as the expert. It explains the dominant ideas from computer science and economics underlying the most important results on market design and introduces the main algorithmic questions and combinatorial structures. Methodologies and applications from both the pre-Internet and post-Internet eras are covered in detail. Key chapters discuss the basic notions of efficiency, fairness and incentives, and the way market design seeks solutions guided by normative criteria borrowed from social choice theory.

This book systematically discusses nonlinear interval optimization design theory and methods. Firstly, adopting a mathematical programming theory perspective, it develops an innovative mathematical transformation model to deal with general nonlinear interval uncertain optimization problems, which is able to equivalently convert complex interval uncertain optimization problems to simple deterministic optimization problems. This model is then used as the basis for various interval uncertain optimization algorithms for engineering applications, which address the low efficiency caused by double-layer nested optimization. Further, the book extends the nonlinear interval optimization theory to design problems associated with multiple optimization objectives, multiple disciplines, and parameter dependence, and establishes the corresponding interval optimization models and solution algorithms. Lastly, it uses the proposed interval uncertain optimization models and methods to deal with practical problems in mechanical engineering and related fields, demonstrating the effectiveness of the models and methods.

Many applications, including computer vision, computer arithmetic, deep learning, entanglement in quantum information, graph theory and energy networks, can be successfully tackled within the framework of polynomial optimization, an emerging field with growing research efforts in the last two decades. One key advantage of these techniques is their ability to model a wide range of problems using optimization formulations. Polynomial optimization heavily relies on the moment-sums of squares (moment-SOS) approach proposed by Lasserre, which provides certificates for positive polynomials. On the practical side, however, there is 'no free lunch' and such optimization methods usually encompass severe scalability issues. Fortunately, for many applications, including the ones formerly mentioned, we can look at the problem in the eyes and exploit the inherent data structure arising from the cost and constraints describing the problem.This book presents several research efforts to resolve this scientific challenge with important computational implications. It provides the development of alternative optimization schemes that scale well in terms of computational complexity, at least in some identified class of problems. It also features a unified modeling framework to handle a wide range of applications involving both commutative and noncommutative variables, and to solve concretely large-scale instances. Readers will find a practical section dedicated to the use of available open-source software libraries.This interdisciplinary monograph is essential reading for students, researchers and professionals interested in solving optimization problems with polynomial input data.

This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Krakow, Poland in 2013. Each chapter in this book exhibits a comprehensive look at new theoretical and/or application-oriented results in mathematical modeling, optimization, and optimal control. Students and researchers involved in image processing, partial differential inclusions, shape optimization, or optimal control theory and its applications to medical and rehabilitation technology, will find this book valuable. The first chapter by Martin Burger provides an overview of recent developments related to Bregman distances, which is an important tool in inverse problems and image processing. The chapter by Piotr Kalita studies the operator version of a first order in time partial differential inclusion and its time discretization. In the chapter by Gunter Leugering, Jan Sokolowski and Antoni Zochowski, nonsmooth shape optimization problems for variational inequalities are considered. The next chapter, by Katja Mombaur is devoted to applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of medical devices. The final chapter, by Nikolai Osmolovskii and Helmut Maurer provides a survey on no-gap second order optimality conditions in the calculus of variations and optimal control, and a discussion of their further development.

This textbook provides a hands-on treatment of the subject of optimization. A comprehensive set of problems and exercises makes it suitable for use in one or two semesters of an advanced undergraduate course or a first-year graduate course. Each half of the book contains a full semester's worth of complementary yet stand-alone material. The practical orientation of the topics chosen and a wealth of useful examples also make the book suitable as a reference work for practitioners in the field. In this second edition the authors have added sections on recent innovations, techniques, and methodologies.

This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.

In a series of conversational essays, this textbook discusses the manner in which economic thought addresses a broad array of everyday issues beyond classical textbook treatments. In the spirit of popular economics books, the author uncovers economic issues and solutions from individuals, businesses, society, and the country as a whole in a decidedly non-technical and relatable manner. Should the federal government mandate use of child safety seats on commercial airlines? Can genetic information substitute for a college degree? The contents of this book touch on many of these contemporary topics in an accessible way. Addressing undergraduate and graduate students, as well as scholars in different fields of economics, this book is a must-read for everybody interested in a better understanding of economic thought.

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

This book is a detailed introduction to selective maintenance and updates readers on recent advances in this field, emphasizing mathematical formulation and optimization techniques. The book is useful for reliability engineers and managers engaged in the practice of reliability engineering and maintenance management. It also provides references that will lead to further studies at the end of each chapter. This book is a reference for researchers in reliability and maintenance and can be used as an advanced text for students.

This book examines how China's decentralization process has affected and will affect the country's macroeconomic performance and the functioning of the market. With an innovative application of game theory, the author develops an analytical framework that can explain the behaviour of the central and local governments under alternative institutional environments. The study also suggests how to establish desirable rules of games in China's political and economic institutions through appropriate reforms.

This book provides a comprehensive study of asymmetric territorial conflict combining game theory, statistical empirical analysis and historiographic analysis. It proposes a model to explain the dynamics of territorial conflict between rivals with a wide disparity in capabilities between them. Using the Israeli-Palestinian conflict as a case study and testing the model on a database of almost four hundred territorial conflicts, Resnick argues that changes in 'patience' - explained by parallel evolutionary processes occurring in the respectively strong and weak societies - underlie the changing behaviour witnessed in such rivalries. Located within the general context of the interplay between material constraints and ideas, the theoretical significance of this model goes beyond the context of territorial conflict and can be seen to provide an explanation for the ideational aspects of power transitions and change in world politics.This book constitutes a significant advance in the literature on territorial conflict, which has increasingly come to be recognized as a key field of enquiry in the discipline of conflict studies and international relations scholarship in general.

This book presents a panorama about the recent progress of industrial mathematics from the point of view of both industrials and researchers. The chapters correspond to a selection of the contributions presented in the "Industry Day" and in the Minisymposium "EU - MATHS - IN: Success Stories of Applications of Mathematics to Industry" organized in the framework of the International Conference ICIAM 2019 held in Valencia (Spain) on July 15-19, 2019. In the Industry Day, included for the first time in this series of Conferences, representatives of companies from different countries and several sectors presented their view about the benefits regarding the usage of mathematical tools and/or collaboration with mathematicians. The contributions of this special session were addressed to industry people. Minisymposium contributions detailed some collaborations between mathematicians and industrials that led to real benefits in several European companies. All the speakers were affiliated in some of the European National Networks that constitute the European Service Network of Mathematics for Industry and Innovation (EU-MATHS-IN).

Optimization has long been a source of both inspiration and applications for geometers, and conversely, discrete and convex geometry have provided the foundations for many optimization techniques, leading to a rich interplay between these subjects. The purpose of the Workshop on Discrete Geometry, the Conference on Discrete Geometry and Optimization, and the Workshop on Optimization, held in September 2011 at the Fields Institute, Toronto, was to further stimulate the interaction between geometers and optimizers. This volume reflects the interplay between these areas.

The inspiring Fejes Toth Lecture Series, delivered by Thomas Hales of the University of Pittsburgh, exemplified this approach. While these fields have recently witnessed a lot of activity and successes, many questions remain open. For example, Fields medalist Stephen Smale stated that the question of the existence of a strongly polynomial time algorithm for linear optimization is one of the most important unsolved problems at the beginning of the 21st century. The broad range of topics covered in this volume demonstrates the many recent and fruitful connections between different approaches, and features novel results and state-of-the-art surveys as well as open problems. "

This book presents a structured approach to formulate, model, and solve mathematical optimization problems for a wide range of real world situations. Among the problems covered are production, distribution and supply chain planning, scheduling, vehicle routing, as well as cutting stock, packing, and nesting. The optimization techniques used to solve the problems are primarily linear, mixed-integer linear, nonlinear, and mixed integer nonlinear programming. The book also covers important considerations for solving real-world optimization problems, such as dealing with valid inequalities and symmetry during the modeling phase, but also data interfacing and visualization of results in a more and more digitized world. The broad range of ideas and approaches presented helps the reader to learn how to model a variety of problems from process industry, paper and metals industry, the energy sector, and logistics using mathematical optimization techniques.

This book focuses on a development of optimal, flexible, and efficient models and algorithms for cell formation in group technology. Its main aim is to provide a reliable tool that can be used by managers and engineers to design manufacturing cells based on their own preferences and constraints imposed by a particular manufacturing system. This tool could potentially lower production costs by minimizing other costs in a number of areas, thereby increasing profit in a manufacturing system. In the volume, the cell formation problem is considered in a systematic and formalized way, and several models are proposed, both heuristic and exact. The models are based on general clustering problems, and are flexible enough to allow for various objectives and constraints. The authors also provide results of numerical experiments involving both artificial data from academic papers in the field and real manufacturing data to certify the appropriateness of the models proposed. The book was intended to suit the broadest possible audience, and thus all algorithmic details are given in a detailed description with multiple numerical examples and informal explanations are provided for the theoretical results. In addition to managers and industrial engineers, this book is intended for academic researchers and students. It will also be attractive to many theoreticians, since it addresses many open problems in computer science and bioinformatics.

As with the previous editions, this fourth edition relies on teaching by example and the Karplus Learning Cycle to convey the ideas of game theory in a way that is approachable, intuitive, and interdisciplinary. Noncooperative equilibrium concepts such as Nash equilibrium, mixed strategy equilibria, and subgame perfect equilibrium are systematically introduced in the first half of the book. Bayesian Nash equilibrium is briefly introduced. The subsequent chapters discuss cooperative solutions with and without side payments, rationalizable strategies and correlated equilibria, and applications to elections, social mechanism design, and larger-scale games. New examples include panic buying, supply-chain shifts in the pandemic, and global warming.

This volume presents extensive research devoted to a broad spectrum of mathematics with emphasis on interdisciplinary aspects of Optimization and Probability. Chapters also emphasize applications to Data Science, a timely field with a high impact in our modern society. The discussion presents modern, state-of-the-art, research results and advances in areas including non-convex optimization, decentralized distributed convex optimization, topics on surrogate-based reduced dimension global optimization in process systems engineering, the projection of a point onto a convex set, optimal sampling for learning sparse approximations in high dimensions, the split feasibility problem, higher order embeddings, codifferentials and quasidifferentials of the expectation of nonsmooth random integrands, adjoint circuit chains associated with a random walk, analysis of the trade-off between sample size and precision in truncated ordinary least squares, spatial deep learning, efficient location-based tracking for IoT devices using compressive sensing and machine learning techniques, and nonsmooth mathematical programs with vanishing constraints in Banach spaces. The book is a valuable source for graduate students as well as researchers working on Optimization, Probability and their various interconnections with a variety of other areas. Chapter 12 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Two approaches are known for solving large-scale unconstrained optimization problems-the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.

This second edition of Lessons in Play reorganizes the presentation of the popular original text in combinatorial game theory to make it even more widely accessible. Starting with a focus on the essential concepts and applications, it then moves on to more technical material. Still written in a textbook style with supporting evidence and proofs, the authors add many more exercises and examples and implement a two-step approach for some aspects of the material involving an initial introduction, examples, and basic results to be followed later by more detail and abstract results. Features Employs a widely accessible style to the explanation of combinatorial game theory Contains multiple case studies Expands further directions and applications of the field Includes a complete rewrite of CGSuite material

This book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course.

Systems with mechanical degrees of freedom containing unstable objects are analysed in this monograph and algorithms for their control are developed, discussed, and numerically tested. This is achieved by identifying unstable modes of motion and using all available resources to suppress them. By using this approach the region of states from which a stable regime can be reached is maximised. The systems discussed in this book are models for pendula and vehicles and find applications in mechatronics, robotics as well as in mechanical and automotive engineering.

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal analogy between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation.

Evolutionary algorithms are very powerful techniques used to find solutions to real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run.

• Comprehensive coverage of this growing area of research
• Carefully introduces each algorithm with examples and in-depth discussion
• Includes many applications to real-world problems, including engineering design anf scheduling
• Accessible to those with limited knowledge of multi-objective optimization and evolutionary algorithms

'Deb's book is complete, eminently readable, and the coverage is scholarly and thorough. It is my pleasure and duty to urge you to buy this book, read it, use it and enjoy it' - David E. Goldberg, University of Illinois at Urbana-Champaign, USA

Here is a collection of nonlinear optimization applications from the real world, expressed in the General Algebraic Modeling System (GAMS). The concepts are presented so that the reader can quickly modify and update them to represent real-world situations.