Optimization problems are of great importance across a broad range of fields. They can be tackled, for example, by approximate algorithms such as metaheuristics. This book is intended both to provide an overview of hybrid metaheuristics to novices of the field, and to provide researchers from the field with a collection of some of the most interesting recent developments. The authors involved in this book are among the top researchers in their domain.

Reinhard Selten, to date the only German Nobel Prize laureate in economics, celebrates his 80th birthday in 2010. While his contributions to game theory are well-known, the behavioral side of his scientific work has received less public exposure, even though he has been committed to experimental research during his entire career, publishing more experimental than theoretical papers in top-tier journals. This Festschrift is dedicated to Reinhard Selten's exceptional influence on behavioral and experimental economics. In this collection of academic highlight papers, a number of his students are joined by leading scholars in experimental research to document the historical role of the "Meister" in the development of the research methodology and of several sub-fields of behavioral economics. Next to the academic insight in these highly active fields of experimental research, the papers also provide a glance at Reinhard Selten's academic and personal interaction with his students and peers.

This monograph describes a new family of algorithms for the simultaneous localization and mapping (SLAM) problem in robotics, called FastSLAM. The FastSLAM-type algorithms have enabled robots to acquire maps of unprecedented size and accuracy, in a number of robot application domains and have been successfully applied in different dynamic environments, including a solution to the problem of people tracking.

This work gathers a selection of outstanding papers presented at the 25th Conference on Differential Equations and Applications / 15th Conference on Applied Mathematics, held in Cartagena, Spain, in June 2017. It supports further research into both ordinary and partial differential equations, numerical analysis, dynamical systems, control and optimization, trending topics in numerical linear algebra, and the applications of mathematics to industry. The book includes 14 peer-reviewed contributions and mainly addresses researchers interested in the applications of mathematics, especially in science and engineering. It will also greatly benefit PhD students in applied mathematics, engineering and physics.

Agent-based modeling and social simulation have emerged as an interdisciplinary area of social science that includes computational economics, organizational science, social dynamics, and complex systems. This area contributes to enriching our understanding of the fundamental processes of social phenomena caused by complex interactions among agents. Bringing together diverse approaches to social simulation and research agendas, this book presents a unique collection of contributions from the Second World Congress on Social Simulation, held in 2008 at George Mason University in Washington DC, USA. This book in particular includes articles on norms, diffusion, social networks, economy, markets and organizations, computational modeling, and programming environments, providing new hypotheses and theories, new simulation experiments compared with various data sets, and new methods for model design and development. These works emerged from a global and interdisciplinary scientific community of the three regional scientific associations for social simulation: the North American Association for Computational Social and Organizational Science (NAACSOS; now the Computational Social Science Society, CSSS), the European Social Simulation Association (ESSA), and the Pacific Asian Association for Agent-bBased Approach in Social Systems Sciences (PAAA)."

This Volume discusses the underlying principles and analysis of the different concepts associated with an emerging socio-inspired optimization tool referred to as Cohort Intelligence (CI). CI algorithms have been coded in Matlab and are freely available from the link provided inside the book. The book demonstrates the ability of CI methodology for solving combinatorial problems such as Traveling Salesman Problem and Knapsack Problem in addition to real world applications from the healthcare, inventory, supply chain optimization and Cross-Border transportation. The inherent ability of handling constraints based on probability distribution is also revealed and proved using these problems.

Mathematical optimization is used in nearly all computer graphics applications, from computer vision to animation. This book teaches readers the core set of techniques that every computer graphics professional should understand in order to envision and expand the boundaries of what is possible in their work.
Study of this authoritative reference will help readers develop a very powerful tool- the ability to create and decipher mathematical models that can better realize solutions to even the toughest problems confronting computer graphics community today.
The authors are renowned researchers from IMPA, the Brazilian National Institute for Pure and Applied Mathematics.
*Distils down a vast and complex world of info on optimization into one short, self-contained volume especially for computer graphics
*Helps CG professionals identify the best technique for solving particular problems quickly, by categorizing the most effective algorithms by application
*Keeps readers current by supplementing the focus on key, classic methods with special end-of-chapter sections on cutting-edge developments

The book brings together an overview of standard concepts in cooperative game theory with applications to the analysis of social networks and hierarchical authority organizations. The standard concepts covered include the multi-linear extension, the Core, the Shapley value, and the cooperative potential. Also discussed are the Core for a restricted collection of formable coalitions, various Core covers, the Myerson value, value-based potentials, and share potentials. Within the context of social networks this book discusses the measurement of centrality and power as well as allocation rules such as the Myerson value and hierarchical allocation rules. For hierarchical organizations, two basic approaches to the exercise of authority are explored; for each approach the allocation of the generated output is developed. Each chapter is accompanied by a problem section, allowing this book to be used as a textbook for an advanced graduate course on game theory.

This volume contains the proceedings of the XII Symposium of Probability and Stochastic Processes which took place at Universidad Autonoma de Yucatan in Merida, Mexico, on November 16-20, 2015. This meeting was the twelfth meeting in a series of ongoing biannual meetings aimed at showcasing the research of Mexican probabilists as well as promote new collaborations between the participants. The book features articles drawn from different research areas in probability and stochastic processes, such as: risk theory, limit theorems, stochastic partial differential equations, random trees, stochastic differential games, stochastic control, and coalescence. Two of the main manuscripts survey recent developments on stochastic control and scaling limits of Markov-branching trees, written by Kazutoshi Yamasaki and Benedicte Haas, respectively. The research-oriented manuscripts provide new advances in active research fields in Mexico. The wide selection of topics makes the book accessible to advanced graduate students and researchers in probability and stochastic processes.

Bestselling author and worst-drawing artist Ben Orlin expands his oeuvre with this interactive collection of mathematical games. With 70-plus games, each taking a minute to learn and a lifetime to master, this treasure trove will delight, educate, and entertain. From beloved math popularizer Ben Orlin comes a masterfully compiled collection of dozens of playable mathematical games. This ultimate game chest draws on mathematical curios, childhood classics, and soon-to-be classics, each hand-chosen to be (1) fun, (2) thought-provoking, and (3) easy to play. With just paper, pens, and the occasional handful of coins, you and a partner can enjoy hours of fun-and hours of challenge. Orlin's sly humor, expansive knowledge, and so-bad-they're-good drawings show us how simple rules summon our best thinking. Games include: * Ultimate Tic-Tac-Toe * Sprouts * Battleship * Quantum Go Fish * Dots and Boxes * Black Hole * Order and Chaos * Sequencium * Paper Boxing * Prophecies * Arpeggios * Banker * Francoprussian Labyrinth * Cats and Dogs * And many more.

This book presents an overview of the differential evolution algorithm. In the last few years the evolutionary computation domain has developed rapidly, and differential evolution is one of the representatives of this domain. It is a recently invented evolutionary algorithm that is gaining more and more popularity. Originally proposed for continuous unconstraint optimization, it was enlarged both for mixed optimization and for handling nonlinear constraints. Later on, new strategies, tuning, and adaptation of control parameters, ways of hybridization were elaborated. Attempts at theoretical analysis were accomplished as well. Moreover, the algorithm has a huge number of practical applications in different areas of science and industry.

This state-of-the-art collection of papers on the theory of Cournotian competition focuses on two main subjects: oligopolistic Cournot competition and contests. The contributors present various applications of the Cournotian Equilibrium Theory, addressing topics such as equilibrium existence and uniqueness, equilibrium structure, dynamic processes, coalitional behavior and welfare. Special emphasis is placed on the aggregative nature of the games that are relevant to such theory. This contributed volume was written to celebrate the 80th birthday of Prof. Koji Okuguchi, a pioneer in oligopoly theory.

Optimal analysis is defined as an analysis that creates and uses sparse, well-structured and well-conditioned matrices. The focus is on efficient methods for eigensolution of matrices involved in static, dynamic and stability analyses of symmetric and regular structures, or those general structures containing such components. Powerful tools are also developed for configuration processing, which is an important issue in the analysis and design of space structures and finite element models.
Different mathematical concepts are combined to make the optimal analysis of structures feasible. Canonical forms from matrix algebra, product graphs from graph theory and symmetry groups from group theory are some of the concepts involved in the variety of efficient methods and algorithms presented.
The algorithms elucidated in this book enable analysts to handle large-scale structural systems by lowering their computational cost, thus fulfilling the requirement for faster analysis and design of future complex systems. The value of the presented methods becomes all the more evident in cases where the analysis needs to be repeated hundreds or even thousands of times, as for the optimal design of structures by different metaheuristic algorithms.
The book is of interest to anyone engaged in computer-aided analysis and design and software developers in this field. Though the methods are demonstrated mainly through skeletal structures, continuum models have also beenadded to show the generality of the methods. The concepts presented are not only applicable to different types of structures but can also be used for the analysis of other systems such as hydraulic and electrical networks."

This book presents an intelligent, integrated, problem-independent method for multiresponse process optimization. In contrast to traditional approaches, the idea of this method is to provide a unique model for the optimization of various processes, without imposition of assumptions relating to the type of process, the type and number of process parameters and responses, or interdependences among them. The presented method for experimental design of processes with multiple correlated responses is composed of three modules: an expert system that selects the experimental plan based on the orthogonal arrays; the factor effects approach, which performs processing of experimental data based on Taguchi's quality loss function and multivariate statistical methods; and process modeling and optimization based on artificial neural networks and metaheuristic optimization algorithms. The implementation is demonstrated using four case studies relating to high-tech industries and advanced, non-conventional processes.

This book provides a detailed understanding of optimization methods as they are implemented in a variety of manufacturing, fabrication and machining processes. It covers the implementation of statistical methods, multi-criteria decision making methods and evolutionary techniques for single and multi-objective optimization to improve quality, productivity, and sustainability in manufacturing. It reports on the theoretical aspects, special features, recent research and latest development in the field. Optimization of Manufacturing Processes is a valuable source of information for researchers and practitioners, as it fills the gap where no dedicated book is available on intelligent manufacturing/modeling and optimization in manufacturing. Readers will develop an understanding of the implementation of statistical and evolutionary techniques for modeling and optimization in manufacturing.

Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysis

Provides a good introduction to the topic

In recent years there has been an explosion of research into linear programming, as well as further steady advances in integer programming. This research has been reported in the research literature but there has been little done from the view of a "combined whole". This book aims to overcome this. With an international authorship of contributors from acknowledged experts in their field, this book provides a clear exposition on such topics as simplex algorithms, and interior point algorithms, both from a theoretical and a computational viewpoint. Surveying recent research that is currently only available in journals this topical book will be of interest not only in the field of mathematics, but also in computer science and operations research as well.

The primary purpose in this book is to present an integrated and innovative methodological approach for the construction and selection of equity portfolios. The approach takes into account the inherent multidimensional nature of the problem, while allowing the decision makers to incorporate specified preferences in the decision processes. A fundamental principle of modern portfolio theory is that comparisons between portfolios are generally made using two criteria; the expected return and portfolio variance. According to most of the portfolio models derived from the stochastic dominance approach, the group of portfolios open to comparisons is divided into two parts: the efficient portfolios, and the dominated. This work integrates the two approaches providing a unified model for decision making in portfolio management with multiple criteria.

The purpose of the science of complexity is to provide, if not a unified approach, at least useful tools to tackling complex problems in various scientific domains. Generally, complexity is considered a fundamental challenge to the reductionist approach in science as a whole and to its ideas of certainty and randomness.

The overall behaviour of a complex system is different from and more than the sum of its parts. The behaviour of non-linear complex systems depends on the interaction (often with retroactive effects) among its constituent parts and not so much (or not only) on the characteristics of these parts themselves; the sum of the behaviour of single parts does not necessarily provide us with an explanation of the aggregate behaviour of a system.

All this is true for economic systems. These are based on the activities of single economic agents. Each individual can obtain only partial knowledge that is focussed around its "world" (local information) and react to external shocks in different ways (local rationality).

The aim of this book is to provide an overview to recent developments in theory and empirical research that view economic systems as complex phenomena whose aggregate dynamics can often not be inferred from its microscopic (microeconomic) building blocks. The collection of papers represented in this volume is dedicated to the memory of Massimo Salzano, who has been a fervent and eloquent advocate of the complexity approach.

The contributions have been presented at a conference held to celebrate Massimo's 60th birthday (Ecople -Economics: From Tradition of Complexity, Capri, 2-4 June, 2006), one year before he unexpectedly passed away in 2007.

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 represents the results of cross-fertilization between OR/MS and CS/AI. It is this interface of OR/CS that makes possible advances that could not have been achieved in isolation. Taken collectively, these articles are indicative of the state-of-the-art in the interface between OR/MS and CS/AI and of the high caliber of research being conducted by members of the INFORMS Computing Society.

Global Optimization has emerged as one of the most exciting new areas of mathematical programming. Global optimization has received a wide attraction from many fields in the past few years, due to the success of new algorithms for addressing previously intractable problems from diverse areas such as computational chemistry and biology, biomedicine, structural optimization, computer sciences, operations research, economics, and engineering design and control. This book contains refereed invited papers submitted at the 4th international confer ence on Frontiers in Global Optimization held at Santorini, Greece during June 8-12, 2003. Santorini is one of the few sites of Greece, with wild beauty created by the explosion of a volcano which is in the middle of the gulf of the island. The mystic landscape with its numerous mult-extrema, was an inspiring location particularly for researchers working on global optimization. The three previous conferences on "Recent Advances in Global Opti mization," "State-of-the-Art in Global Optimization," and "Optimization in Computational Chemistry and Molecular Biology: Local and Global approaches" took place at Princeton University in 1991, 1995, and 1999, respectively. The papers in this volume focus on de terministic methods for global optimization, stochastic methods for global optimization, distributed computing methods in global optimization, and applications of global optimiza tion in several branches of applied science and engineering, computer science, computational chemistry, structural biology, and bio-informatics."

This book was written mainly during the Spring periods of 2008 and 2009, when the ?rst author was visiting Maastricht University. Financial s- port both from the Dutch Science Foundation NWO (grants 040. 11. 013 and 0. 40. 11. 082) and from the research institute METEOR (Maastricht Univ- sity) is gratefully acknowledged. Jerusalem Bezalel Peleg Maastricht Hans Peters April 2010 v Contents Preview to this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Part I Representations of constitutions 1 Introduction to Part I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 2 Arrow's constitution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 3 Arrow's Impossibility Theorem and its implications. . . . . . . . . 4 1. 4 Ga ]rdenfors's model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 5 Notes and comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Constitutions, e?ectivity functions, and game forms . . . . . . 7 2. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2. 2 Constitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2. 3 Constitutions and e?ectivity functions . . . . . . . . . . . . . . . . . . . . 12 2. 4 Game forms and a representation theorem. . . . . . . . . . . . . . . . . 16 2. 5 Representation and simultaneous exercising of rights. . . . . . . . 19 2. 6 Notes and comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Nash consistent representations. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3. 2 Existence of Nash consistent representations: a general result 22 3. 3 The case of ?nitely many alternatives. . . . . . . . . . . . . . . . . . . . . 24 3. 4 Nash consistent representations of topological e?ectivity functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. 5 Veto functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3. 5. 1 Finitely many alternatives. . . . . . . . . . . . . . . . . . . . . . . . . 34 3. 5. 2 Topological veto functions. . . . . . . . . . . . . . . . . . . . . . . . . 36 3. 6 Liberalism and Pareto optimality of Nash equilibria. . . . . . . . . 40 3. 7 Notes and comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 vii viii Contents 4 Acceptable representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ."

Optimization Theory is becoming a more and more important mathematical as well as interdisciplinary area, especially in the interplay between mathematics and many other sciences like computer science, physics, engineering, operations research, etc.
This volume gives a comprehensive introduction into the theory of (deterministic) optimization on an advanced undergraduate and graduate level. One main feature is the treatment of both continuous and discrete optimization at the same place. This allows to study the problems under different points of view, supporting a better understanding of the entire field.
Audience: The book can be adapted well as an introductory textbook into optimization theory on a basis of a two semester course; however, each of its parts can also be taught separately. Many exercises are included to increase the reader's understanding.

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