There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by the General Secretariat of Research and Tech nology of Greece, by the Ministry of Education of Greece, and several local Greek government agencies and companies. This volume contains a selective collection of refereed papers based on invited and contribut ing talks presented at this conference. The two themes of convexity and global optimization pervade this book. The conference provided a forum for researchers working on different aspects of convexity and global opti mization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming."

The mathematical theory of democracy deals with selection of representatives who make decisions on behalf of the whole society. In this book, the notion of representativeness is operationalized with the index of popularity (the average percentage of the population whose opinion is represented on a number of issues) and the index of universality (the frequency of cases when the opinion of a majority is represented). These indices are applied to evaluate and study the properties of single representatives (e.g. president) and representative bodies (e.g. parliament, magistrate, cabinet, jury, coalition). To bridge representative and direct democracy, an election method is proposed that is based not on voting but on indexing candidates with respect to the electorate's political profile. In addition, societal and non-societal applications are considered.

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners - including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers - are interested in solving large-scale MINLP instances.

This book is concerned with situations in which several persons reach decisions independently and the final consequence depends, potentially, upon each of the decisions taken. Such situations may be described formally by an extensive form game: a mathematical object which specifies the order in which decisions are to be taken, the information available to the decision makers at each point in time, and the consequence that results for each possible combination of decisions. A necessary requirement for rational behavior in such games is that each decision maker should reach a decision that is optimal, given his preferences over his own decisions. This requirement is far from sufficient, however, since every decision maker should in addition base his preferences upon the conjecture that his opponents will act optimally as well. It is this principle that distinguishes noncooperative game theory from one-person decision theory. The main purpose of Rationality in Extensive Form Games is to discuss different formalizations of this principle in extensive form games, such as backward induction, Nash equilibrium, forward induction and rationalizability, under the assumption that the decision makers' preferences are given by subjective expected utility functions. The various formalizations, or rationality criteria, are illustrated by examples, and the relationships among the different criteria are explored.

Performance evaluation of increasingly complex human-made systems requires the use of simulation models. However, these systems are difficult to describe and capture by succinct mathematical models. The purpose of this book is to address the difficulties of the optimization of complex systems via simulation models or other computation-intensive models involving possible stochastic effects and discrete choices. This book establishes distinct advantages of the "softer" ordinal approach for search-based type problems, analyzes its general properties, and shows the many orders of magnitude improvement in computational efficiency that is possible.

The developments within the computationally and numerically oriented ar eas of Operations Research, Finance, Statistics and Economics have been sig nificant over the past few decades. Each area has been developing its own computer systems and languages that suit its needs, but there is relatively little cross-fertilization among them yet. This volume contains a collection of papers that each highlights a particular system, language, model or paradigm from one of the computational disciplines, aimed at researchers and practitioners from the other fields. The 15 papers cover a number of relevant topics: Models and Modelling in Operations Research and Economics, novel High-level and Object-Oriented approaches to programming, through advanced uses of Maple and MATLAB, and applications and solution of Differential Equations in Finance. It is hoped that the material in this volume will whet the reader's appetite for discovering and exploring new approaches to old problems, and in the longer run facilitate cross-fertilization among the fields. We would like to thank the contributing authors, the reviewers, the publisher, and last, but not least, Jesper Saxtorph, Anders Nielsen, and Thomas Stidsen for invaluable technical assistance."

This book focuses on optimal control and systems engineering in the big data era. It examines the scientific innovations in optimization, control and resilience management that can be applied to further success. In both business operations and engineering applications, there are huge amounts of data that can overwhelm computing resources of large-scale systems. This "big data" provides new opportunities to improve decision making and addresses risk for individuals as well in organizations. While utilizing data smartly can enhance decision making, how to use and incorporate data into the decision making framework remains a challenging topic. Ultimately the chapters in this book present new models and frameworks to help overcome this obstacle. Optimization and Control for Systems in the Big-Data Era: Theory and Applications is divided into five parts. Part I offers reviews on optimization and control theories, and Part II examines the optimization and control applications. Part III provides novel insights and new findings in the area of financial optimization analysis. The chapters in Part IV deal with operations analysis, covering flow-shop operations and quick response systems. The book concludes with final remarks and a look to the future of big data related optimization and control problems.

During the last decade I have explored the consequences of what I have chosen to call the 'consistent preferences' approach to deductive reasoning in games. To a great extent this work has been done in coop eration with my co-authors Martin Dufwenberg, Andres Perea, and Ylva Sovik, and it has lead to a series of journal articles. This book presents the results of this research program. Since the present format permits a more extensive motivation for and presentation of the analysis, it is my hope that the content will be of interest to a wider audience than the corresponding journal articles can reach. In addition to active researcher in the field, it is intended for graduate students and others that wish to study epistemic conditions for equilibrium and rationalizability concepts in game theory. Structure of the book This book consists of twelve chapters. The main interactions between the chapters are illustrated in Table 0.1. As Table 0.1 indicates, the chapters can be organized into four dif ferent parts. Chapters 1 and 2 motivate the subsequent analysis by introducing the 'consistent preferences' approach, and by presenting ex amples and concepts that are revisited throughout the book. Chapters 3 and 4 present the decision-theoretic framework and the belief operators that are used in later chapters. Chapters 5, 6, 10, and 11 analyze games in the strategic form, while the remaining chapters-Chapters 7, 8, 9, and 12-are concerned with games in the extensive form.

This introduction to the field of hyper-heuristics presents the required foundations and tools and illustrates some of their applications. The authors organized the 13 chapters into three parts. The first, hyper-heuristic fundamentals and theory, provides an overview of selection constructive, selection perturbative, generation constructive and generation perturbative hyper-heuristics, and then a formal definition of hyper-heuristics. The chapters in the second part of the book examine applications of hyper-heuristics in vehicle routing, nurse rostering, packing and examination timetabling. The third part of the book presents advanced topics and then a summary of the field and future research directions. Finally the appendices offer details of the HyFlex framework and the EvoHyp toolkit, and then the definition, problem model and constraints for the most tested combinatorial optimization problems. The book will be of value to graduate students, researchers, and practitioners.

This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 17-19, 2016. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of deterministic and stochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.

This book discusses mathematical models for various applications in economics, with a focus on non-linear dynamics. Based on the author's over 50 years of active work in the field, the book has been inspired by models from the period between 1920 and 1950. Following a brief introduction to economics for mathematicians and other modelers, it assembles a repository of useful specific functions for global dynamic modeling. Furthermore, twelve "research stubs" - outlined research agendas that have not yet been fully worked on - are suggested for further study and could even be expanded to entire research projects. The book is a valuable resource, particularly for young scientists who are skilled in mathematical and computational techniques and are looking for applications in economics.

The primary goal of this book is to present the research findings and conclusions of physicists, economists, mathematicians and financial engineers working in the field of "Econophysics" who have undertaken agent-based modelling, comparison with empirical studies and related investigations.
Most standard economic models assume the existence of the representative agent, who is "perfectly rational" and applies the utility maximization principle when taking action. One reason for this is the desire to keep models mathematically tractable: no tools are available to economists for solving non-linear models of heterogeneous adaptive agents without explicit optimization. In contrast, multi-agent models, which originated from statistical physics considerations, allow us to go beyond the prototype theories of traditional economics involving the representative agent. This book is based on the Econophys-Kolkata VII Workshop, at which many such modelling efforts were presented. In the book, leading researchers in their fields report on their latest work, consider recent developments and review the contemporary literature.

Essays on Cooperative Games collates selected contributions on Cooperative Games. The papers cover both theoretical aspects (Coalition Formation, Values, Simple Games and Dynamic Games) and applied aspects (in Finance, Production, Transportation and Market Games). A contribution on Minimax Theorem (by Ken Binmore) and a brief history of early Game Theory (by Gianfranco Gambarelli and Guillermo Owen) are also enclosed.

This book on optimization includes forewords by Michael I. Jordan, Zongben Xu and Zhi-Quan Luo. Machine learning relies heavily on optimization to solve problems with its learning models, and first-order optimization algorithms are the mainstream approaches. The acceleration of first-order optimization algorithms is crucial for the efficiency of machine learning. Written by leading experts in the field, this book provides a comprehensive introduction to, and state-of-the-art review of accelerated first-order optimization algorithms for machine learning. It discusses a variety of methods, including deterministic and stochastic algorithms, where the algorithms can be synchronous or asynchronous, for unconstrained and constrained problems, which can be convex or non-convex. Offering a rich blend of ideas, theories and proofs, the book is up-to-date and self-contained. It is an excellent reference resource for users who are seeking faster optimization algorithms, as well as for graduate students and researchers wanting to grasp the frontiers of optimization in machine learning in a short time.

Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of decision variables under continuous perturbations of the parameters. Perturbations that preserve this continuity are regions of stability. It is shown how these regions can be identified. The main results on stability are characterizations of locally and globally optimal parameters for stable and also for unstable perturbations. The results are straightened for linear models and bi-level programs. Some of the results are extended to abstract spaces after considering parameters as controls'. Illustrations from diverse fields, such as data envelopment analysis, management, von Stackelberg games of market economy, and navigation problems are given and several case studies are solved by finding optimal parameters. The book has been written in an analytic spirit. Many results appear here for the first time in book form. Audience: The book is written at the level of a first-year graduate course in optimization for students with varied backgrounds interested in modeling of real-life problems. It is expected that the reader has been exposed to a prior elementary course in optimization, such as linear or non-linear programming. The last section of the book requires some knowledge of functional analysis.

Today it appears that we understand more about the universe than about our interconnected socio-economic world. In order to uncover organizational structures and novel features in these systems, we present the first comprehensive complex systems analysis of real-world ownership networks. This effort lies at the interface between the realms of economics and the emerging field loosely referred to as complexity science. The structure of global economic power is reflected in the network of ownership ties of companies and the analysis of such ownership networks has possible implications for market competition and financial stability. Thus this work presents powerful new tools for the study of economic and corporate networks that are only just beginning to attract the attention of scholars.

Constrained optimization models are core tools in business, science, government, and the military with applications including airline scheduling, control of petroleum refining operations, investment decisions, and many others. Constrained optimization models have grown immensely in scale and complexity in recent years as inexpensive computing power has become widely available. Models now frequently have many complicated interacting constraints, giving rise to a host of issues related to feasibility and infeasibility. For example, it is sometimes difficult to find any feasible point at all for a large model, or even to accurately determine if one exists, e.g. for nonlinear models. If the model is feasible, how quickly can a solution be found? If the model is infeasible, how can the cause be isolated and diagnosed? Can a repair to restore feasibility be carried out automatically? Researchers have developed numerous algorithms and computational methods in recent years to address such issues, with a number of surprising spin-off applications in fields such as artificial intelligence and computational biology. Over the same time period, related approaches and techniques relating to feasibility and infeasibility of constrained problems have arisen in the constraint programming community. Feasibility and Infeasibility in Optimization is a timely expository book that summarizes the state of the art in both classical and recent algorithms related to feasibility and infeasibility in optimization, with a focus on practical methods. All model forms are covered, including linear, nonlinear, and mixed-integer programs. Connections to related work in constraint programming are shown. Part Iof the book addresses algorithms for seeking feasibility quickly, including new methods for the difficult cases of nonlinear and mixed-integer programs. Part II provides algorithms for analyzing infeasibility by isolating minimal infeasible (or maximum feasible) subsets of constraints, or by finding the best repair for the infeasibility. Infeasibility analysis algorithms have arisen primarily over the last two decades, and the book covers these in depth and detail. Part III describes applications in numerous areas outside of direct infeasibility analysis such as finding decision trees for data classification, analyzing protein folding, radiation treatment planning, automated test assembly, etc. A main goal of the book is to impart an understanding of the methods so that practitioners can make immediate use of existing algorithms and software, and so that researchers can extend the state of the art and find new applications. The book is of interest to researchers, students, and practitioners across the applied sciences who are working on optimization problems.

The chapters which appear in this volume are selected studies presented at the First International Conference on Engineering and Applied Sciences Optimization (OPT-i), Kos, Greece, 4-6 June 2014 and works written by friends, former colleagues and students of the late Professor M. G. Karlaftis; all in the area of optimization that he loved and published so much in himself. The subject areas represented here range from structural optimization, logistics, transportation, traffic and telecommunication networks to operational research, metaheuristics, multidisciplinary and multiphysics design optimization, etc. This volume is dedicated to the life and the memory of Professor Matthew G. Karlaftis, who passed away a few hours before he was to give the opening speech at OPT-i. All contributions reflect the warmth and genuine friendship which he enjoyed from his associates and show how much his scientific contribution has been appreciated. He will be greatly missed and it is hoped that this volume will be received as a suitable memorial to his life and achievements.

This book is devoted to geometric methods in the theory of differential equations with quadratic right-hand sides (Riccati-type equations), which are closely related to the calculus of variations and optimal control theory. Connections of the calculus of variations and the Riccati equation with the geometry of Lagrange-Grassmann manifolds and classical Cartan-Siegel homogeneity domains in a space of several complex variables are considered. In the study of the minimization problem for a multiple integral, a quadratic partial differential equation that is an analogue of the Riccati equation in the calculus of varatiations is studied. This book is based on lectures given by the author ower a period of several years in the Department of Mechanics and Mathematics of Moscow State University. The book is addressed to undergraduate and graduate students, scientific researchers and all specialists interested in the problems of geometry, the calculus of variations, and differential equations.

Many complex aeronautical design problems can be formulated with efficient multi-objective evolutionary optimization methods and game strategies. This book describes the role of advanced innovative evolution tools in the solution, or the set of solutions of single or multi disciplinary optimization. These tools use the concept of multi-population, asynchronous parallelization and hierarchical topology which allows different models including precise, intermediate and approximate models with each node belonging to the different hierarchical layer handled by a different Evolutionary Algorithm. The efficiency of evolutionary algorithms for both single and multi-objective optimization problems are significantly improved by the coupling of EAs with games and in particular by a new dynamic methodology named "Hybridized Nash-Pareto games". Multi objective Optimization techniques and robust design problems taking into account uncertainties are introduced and explained in detail. Several applications dealing with civil aircraft and UAV, UCAV systems are implemented numerically and discussed. Applications of increasing optimization complexity are presented as well as two hands-on test cases problems. These examples focus on aeronautical applications and will be useful to the practitioner in the laboratory or in industrial design environments. The evolutionary methods coupled with games presented in this volume can be applied to other areas including surface and marine transport, structures, biomedical engineering, renewable energy and environmental problems. This book will be of interest to students, young scientists and engineers involved in the field of multi physics optimization.

Solving nonsmooth optimization (NSO) problems is critical in many practical applications and real-world modeling systems. The aim of this book is to survey various numerical methods for solving NSO problems and to provide an overview of the latest developments in the field. Experts from around the world share their perspectives on specific aspects of numerical NSO. The book is divided into four parts, the first of which considers general methods including subgradient, bundle and gradient sampling methods. In turn, the second focuses on methods that exploit the problem's special structure, e.g. algorithms for nonsmooth DC programming, VU decomposition techniques, and algorithms for minimax and piecewise differentiable problems. The third part considers methods for special problems like multiobjective and mixed integer NSO, and problems involving inexact data, while the last part highlights the latest advancements in derivative-free NSO. Given its scope, the book is ideal for students attending courses on numerical nonsmooth optimization, for lecturers who teach optimization courses, and for practitioners who apply nonsmooth optimization methods in engineering, artificial intelligence, machine learning, and business. Furthermore, it can serve as a reference text for experts dealing with nonsmooth optimization.

This book features selected papers from The Seventh International Conference on Research and Education in Mathematics that was held in Kuala Lumpur, Malaysia from 25 - 27th August 2015. With chapters devoted to the most recent discoveries in mathematics and statistics and serve as a platform for knowledge and information exchange between experts from academic and industrial sectors, it covers a wide range of topics, including numerical analysis, fluid mechanics, operation research, optimization, statistics and game theory. It is a valuable resource for pure and applied mathematicians, statisticians, engineers and scientists, and provides an excellent overview of the latest research in mathematical sciences.

This book offers a valuable reference guide for researchers in distributed optimization and for senior undergraduate and graduate students alike. Focusing on the natures and functions of agents, communication networks and algorithms in the context of distributed optimization for networked control systems, this book introduces readers to the background of distributed optimization; recent developments in distributed algorithms for various types of underlying communication networks; the implementation of computation-efficient and communication-efficient strategies in the execution of distributed algorithms; and the frameworks of convergence analysis and performance evaluation. On this basis, the book then thoroughly studies 1) distributed constrained optimization and the random sleep scheme, from an agent perspective; 2) asynchronous broadcast-based algorithms, event-triggered communication, quantized communication, unbalanced directed networks, and time-varying networks, from a communication network perspective; and 3) accelerated algorithms and stochastic gradient algorithms, from an algorithm perspective. Finally, the applications of distributed optimization in large-scale statistical learning, wireless sensor networks, and for optimal energy management in smart grids are discussed.

This book is a collection of original papers presented at the International Conference on Computational Mathematics in Nanoelectronics and Astrophysics (CMNA 2018) held at the Indian Institute of Technology Indore, India, from 1 to 3 November 2018. It aims at presenting recent developments of computational mathematics in nanoelectronics, astrophysics and related areas of space sciences and engineering. These proceedings discuss the most advanced innovations, trends and real-world challenges encountered and their solutions with the application of computational mathematics in nanoelectronics, astrophysics and space sciences. From focusing on nano-enhanced smart technological developments to the research contributions of premier institutes in India and abroad on ISRO's future space explorations-this book includes topics from highly interdisciplinary areas of research. The book is of interest to researchers, students and practising engineers working in diverse areas of science and engineering, ranging from applied and computational mathematics to nanoelectronics, nanofabrications and astrophysics.

This volume collects outstanding contributions to the theory of games, the theory of game-theoretical rationality, and their applications. 27 articles present the new situation and the recent advances in game theory after the award of the Nobel Prize in economics and especially in game theory to John F. Nash, John C. Harsanyi, and Reinhard Selten. Two of them, Harsanyi and Selten, have contributed leading articles to this volume. In utility and game theory, the question of which rationality governs their methods and the behavior of the agents as well has emerged as one of the most exciting new conceptual foundations of all social sciences. The main aim of this book is to find an answer to this problem. Do we have to give up our belief in the traditional form of deductive and linear rationality in the social sciences in favor of probabilistic and stochastic methods? Which kind of rationality do we, and should we, use when we attempt to practically solve societal problems and conflicts? Quite a few articles in this book address these questions. The consequences of a new, multi-faceted rationality, which is going to shake the traditional foundation of game theory, decision theory, and utility theory, and, finally, the social sciences in their entirety, are discussed in depth in seven chapters and a preface: Rationality and the Foundations of the Social Sciences, ' Cooperation and Rationality, ' Rationality and Economics, ' Bayesian Theory and Rationality, ' Evolution and Evolutionary Game Theory, ' Ethics and Game Theory, ' and Applications of Game Theory'. The contributors include economists, utility and decision theorists, psychologists, sociologists, physicists, philosophers of sciencesand probability theorists. They attempt to make their contributions accessible to a wide audience. The book will interest researchers, teachers and advanced students in the above-mentioned disciplines; it can be used for a one-semester course on the graduate level. The volume also includes a review section focusing on recent publications on Logical Empiricism and its influence. An autobiographical report on the Vienna Circle by Arne Naess follows the main part of the Yearbook. An overview of the activities of the Institute Vienna Circle 1997/98 concludes the volume.