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.

Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB (R), and Maple (TM) to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.

Differential equations play a noticeable role in engineering, physics, economics, and other disciplines. They permit us to model changing forms in both mathematical and physical problems. These equations are precisely used when a deterministic relation containing some continuously varying quantities and their rates of change in space and/or time is recognized or postulated. This book is intended to provide a straightforward introduction to the concept of partial differential equations. It provides a diversity of numerical examples framed to nurture the intellectual level of scholars. It includes enough examples to provide students with a clear concept and also offers short questions for comprehension. Construction of real-life problems is considered in the last chapter along with applications. Research scholars and students working in the fields of engineering, physics, and different branches of mathematics need to learn the concepts of partial differential equations to solve their problems. This book will serve their needs instead of having to use more complex books that contain more concepts than needed.

Electoral promises help to win votes and political candidates, or parties should strategically choose what they can deliver to win an election. Past game-theoretical studies tend to ignore electoral promises and this book sheds illuminating light on the functions and effects of electoral promises on policies or electoral outcomes through game theory models. This book provides a basic framework for game-theoretical analysis of electoral promises. The book also includes cases to illustrate real life applications of these theories.

Game Theory: A Modeling Approach quickly moves readers through the fundamental ideas of the subject to enable them to engage in creative modeling projects based on game theoretic concepts. The authors match conclusions to real-world scenarios and applications. The text engages students in active learning, group work, in-class discussions and interactive simulations. Each chapter provides foundation pieces or adds more features to help readers build game theoretic models. The chapters include definitions, concepts and illustrative examples. The text will engage and challenge both undergraduate and graduate students. Features: Enables readers to apply game theorty to real-world scenarios Chapters can be used for core course materials or independent stuides Exercises, included at the end of the chapters, follow the order of the sections in the text Select answers and solutions are found at the end of the book Solutions manual for instructors is available from the authors

This important three volume set is a collection of key writings on game theory published before 1963. It makes many frequently-cited and historically important articles conveniently available to a wider audience. The collection includes comprehensive coverage of the game theoretical writings of von Neumann, Nash and Wald. The editors have written a succinct introduction to accompany the articles.

There are thousands of books relating to poker, blackjack, roulette and baccarat, including strategy guides, statistical analysis, psychological studies, and much more. However, there are no books on Pell, Rouleno, Street Dice, and many other games that have had a short life in casinos! While this is understandable - most casino gamblers have not heard of these games, and no one is currently playing them - their absence from published works means that some interesting mathematics and gaming history are at risk of being lost forever. Table games other than baccarat, blackjack, craps, and roulette are called carnival games, as a nod to their origin in actual traveling or seasonal carnivals. Mathematics of Casino Carnival Games is a focused look at these games and the mathematics at their foundation. Features * Exercises, with solutions, are included for readers who wish to practice the ideas presented * Suitable for a general audience with an interest in the mathematics of gambling and games * Goes beyond providing practical 'tips' for gamblers, and explores the mathematical principles that underpin gambling games

This text is based on a lecture course given by the authors in the framework of Oberwolfach Seminars at the Mathematisches Forschungsinstitut Oberwolfach in May, 2013. It is intended to serve as a thorough introduction to the rapidly developing field of positional games. This area constitutes an important branch of combinatorics, whose aim it is to systematically develop an extensive mathematical basis for a variety of two player perfect information games. These ranges from such popular games as Tic-Tac-Toe and Hex to purely abstract games played on graphs and hypergraphs. The subject of positional games is strongly related to several other branches of combinatorics such as Ramsey theory, extremal graph and set theory, and the probabilistic method. These notes cover a variety of topics in positional games, including both classical results and recent important developments. They are presented in an accessible way and are accompanied by exercises of varying difficulty, helping the reader to better understand the theory.The text will benefit both researchers and graduate students in combinatorics and adjacent fields."

Discusses replacement, repair, and inspection Offers estimation and statistical tests Covers accelerated life testing Explores warranty analysis manufacturing Includes service reliability

The H control has been one of the important robust control approaches since the 1980s. This book extends the area to nonlinear stochastic H2/H control, and studies more complex and practically useful mixed H2/H controller synthesis rather than the pure H control. Different from the commonly used convex optimization method, this book applies the Nash game approach to give necessary and sufficient conditions for the existence and uniqueness of the mixed H2/H control. Researchers will benefit from our detailed exposition of the stochastic mixed H2/H control theory, while practitioners can apply our efficient algorithms to address their practical problems.

Offers fundamental theories and practical and more sophisticated applications of Evolutionary Computation in varied industries Provides insight into various platforms, paradigms, techniques, and tools used in Evolutionary Computation for diverse fields Presents an understanding related to optimization, performance tuning, virtualization, deployment models, and their applications Covers a variety of applications for social and essential models and is based on real life examples Useful for decision making based on optimized data through Evolutionary Computation in multi-dimensions

Mathematical Puzzle Tales from Mount Olympus uses fascinating tales from Greek Mythology as the background for introducing mathematics puzzles to the general public. A background in high school mathematics will be ample preparation for using this book, and it should appeal to anyone who enjoys puzzles and recreational mathematics. Features: Combines the arts and science, and emphasizes the fact that mathematics straddles both domains. Great resource for students preparing for mathematics competitions, and the trainers of such students.

Nature-Inspired Optimization Algorithms, a comprehensive work on the most popular optimization algorithms based on nature, starts with an overview of optimization going from the classical to the latest swarm intelligence algorithm. Nature has a rich abundance of flora and fauna that inspired the development of optimization techniques, providing us with simple solutions to complex problems in an effective and adaptive manner. The study of the intelligent survival strategies of animals, birds, and insects in a hostile and ever-changing environment has led to the development of techniques emulating their behavior. This book is a lucid description of fifteen important existing optimization algorithms based on swarm intelligence and superior in performance. It is a valuable resource for engineers, researchers, faculty, and students who are devising optimum solutions to any type of problem ranging from computer science to economics and covering diverse areas that require maximizing output and minimizing resources. This is the crux of all optimization algorithms. Features: Detailed description of the algorithms along with pseudocode and flowchart Easy translation to program code that is also readily available in Mathworks website for some of the algorithms Simple examples demonstrating the optimization strategies are provided to enhance understanding Standard applications and benchmark datasets for testing and validating the algorithms are included This book is a reference for undergraduate and post-graduate students. It will be useful to faculty members teaching optimization. It is also a comprehensive guide for researchers who are looking for optimizing resources in attaining the best solution to a problem. The nature-inspired optimization algorithms are unconventional, and this makes them more efficient than their traditional counterparts.

The progress of society can only happen through interpersonal cooperation, because only cooperation can bring about mutual benefit, thus bringing happiness to each person. This should be our collective rationality, but we often see it conflicts with individual interests, which leads to the so-called "Prisoners' Dilemma" and does not bring happiness to all. From a game theoretical perspective, this book addresses the issue of how people can cooperate better. It has two objectives. The first is to use common language to systematically introduce the basic methodologies and core conclusions of Game Theory, including the Nash equilibrium, multiple equilibriums, dynamic games, etc. Mathematics and theoretical models are used to the minimum necessary scope too, to make this book get access to ordinary readers with elementary mathematical training. The second objective is to utilize these methods and conclusions to analyze various Chinese social issues and institutional arrangements, with a focus on the reasons people exhibit non-cooperative behaviors as well as the institutions and cultures that promote interpersonal cooperation. In addition to economics, specialists in sociology, law, history, politics and management will also be attracted by this book for its insightful analysis on the issue of cooperation in these fields. Also, readers curious about Chinese society will benefit from this book.

This collection of essays represents responses by over eighty scholars to an unusual request: give your high level assessment of the field of economic design, as broadly construed. Where do we come from? Where do we go from here? The book editors invited short, informal reflections expressing deeply felt but hard to demonstrate opinions, unsupported speculation, and controversial views of a kind one might not normally risk submitting for review. The contributors - both senior researchers who have shaped the field and promising, younger researchers - responded with a diverse collection of provocative pieces, including: retrospective assessments or surveys of the field; opinion papers; reflections on critical points for the development of the discipline; proposals for the immediate future; "science fiction"; and many more. The readers should have fun reading these unusual pieces - as much as the contributors enjoyed writing them.

Brian Clegg was always fascinated by Isaac Asimov's classic Foundation series of books, in which the future is predicted using sophisticated mathematical modelling of human psychology and behaviour. Only much later did he realise that Asimov's 'psychohistory' had a real-world equivalent: game theory. Originating in the study of probabilistic gambling games that depend on a random source - the throw of a dice or the toss of a coin - game theory soon came to be applied to human interactions: essentially, what was the best strategy to win, whatever you were doing? Its mathematical techniques have been applied, with varying degrees of wisdom, to fields such as economics, evolution, and questions such as how to win a nuclear war. Clegg delves into game theory's colourful history and significant findings, and shows what we can all learn from this oft-misunderstood field of study.

This is the first comprehensive book on the AIMD algorithm, the most widely used method for allocating a limited resource among competing agents without centralized control. The authors offer a new approach that is based on positive switched linear systems. It is used to develop most of the main results found in the book, and fundamental results on stochastic switched nonnegative and consensus systems are derived to obtain these results. The original and best known application of the algorithm is in the context of congestion control and resource allocation on the Internet, and readers will find details of several variants of the algorithm in order of increasing complexity, including deterministic, random, linear, and nonlinear versions. In each case, stability and convergence results are derived based on unifying principles. Basic and fundamental properties of the algorithm are described, examples are used to illustrate the richness of the resulting dynamical systems, and applications are provided to show how the algorithm can be used in the context of smart cities, intelligent transportation systems, and the smart grid.

Optimization and decision making are integral parts of any manufacturing process and management system. The objective of this book is to demonstrate the confluence of theory and applications of various types of multi-criteria decision making and optimization techniques with reference to textile manufacturing and management. Divided into twelve chapters, it discusses various multi-criteria decision-making methods such as AHP, TOPSIS, ELECTRE, and optimization techniques like linear programming, fuzzy linear programming, quadratic programming, in textile domain. Multi-objective optimization problems have been dealt with two approaches, namely desirability function and evolutionary algorithm. Key Features Exclusive title covering textiles and soft computing fields including optimization and decision making Discusses concepts of traditional and non-traditional optimization methods with textile examples Explores pertinent single-objective and multi-objective optimizations Provides MATLAB coding in the Appendix to solve various types of multi-criteria decision making and optimization problems Includes examples and case studies related to textile engineering and management

This monograph provides a framework for students and practitioners who are working on the solution of electromagnetic imaging in geophysics. Bridging the gap between theory and practical applied material (for example, inverse and forward problems), it provides:* A simple explanation of finite volume discretization.* Basic concepts in solving inverse problems through optimization.* A summary of applied electromagnetics methods.* MATLAB? code for efficient computation.

- Includes industrial case studies - Includes chapters on cyber physical systems, machine learning, deep learning, cyber security, robotics, smart manufacturing and predictive analytics - surveys current trends and challenges in metaheuristics and industry 4.0

Written by experts from all over the world, the book comprises the latest applications of mathematical and models in food engineering and fermentation. It provides the fundamentals on statistical methods to solve standard problems associated with food engineering and fermentation technology. Combining theory with a practical, hands-on approach, this book covers key aspects of food engineering. Presenting cuttingedge information, the book is an essential reference on the fundamental concepts associated with food engineering.

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.

ELEMENTARY LINEAR ALGEBRA, 8E, INTERNATIONAL METRIC EDITION's clear, careful, and concise presentation of material helps you fully understand how mathematics works. The author balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. To engage you in the material, a new design highlights the relevance of the mathematics and makes the book easier to read. Data and applications reflect current statistics and examples, demonstrating the link between theory and practice. The companion website LarsonLinearAlgebra.com offers free access to multiple study tools and resources. CalcChat.com offers free step-by-step solutions to the odd-numbered exercises in the text.

Game Theory and the Law is a collection of previously published articles in which ideas from game theory and the economics of asymmetric information are applied to legal issues. Game theory's method is to simplify a situation by describing it in terms of players, actions, payoffs, after which the players' strategic interactions can be described. Whether used explicitly or implicitly, this is a highly useful approach to law. This important volume collects together the classic articles on the subject together with surveys of the approach and illustrative examples of the use of game theory in law.

Seeking sparse solutions of underdetermined linear systems is required in many areas of engineering and science such as signal and image processing. The efficient sparse representation becomes central in various big or high-dimensional data processing, yielding fruitful theoretical and realistic results in these fields. The mathematical optimization plays a fundamentally important role in the development of these results and acts as the mainstream numerical algorithms for the sparsity-seeking problems arising from big-data processing, compressed sensing, statistical learning, computer vision, and so on. This has attracted the interest of many researchers at the interface of engineering, mathematics and computer science. Sparse Optimization Theory and Methods presents the state of the art in theory and algorithms for signal recovery under the sparsity assumption. The up-to-date uniqueness conditions for the sparsest solution of underdertemined linear systems are described. The results for sparse signal recovery under the matrix property called range space property (RSP) are introduced, which is a deep and mild condition for the sparse signal to be recovered by convex optimization methods. This framework is generalized to 1-bit compressed sensing, leading to a novel sign recovery theory in this area. Two efficient sparsity-seeking algorithms, reweighted l1-minimization in primal space and the algorithm based on complementary slackness property, are presented. The theoretical efficiency of these algorithms is rigorously analysed in this book. Under the RSP assumption, the author also provides a novel and unified stability analysis for several popular optimization methods for sparse signal recovery, including l1-mininization, Dantzig selector and LASSO. This book incorporates recent development and the author's latest research in the field that have not appeared in other books.