In many decision problems, e.g. from the area of production and logistics manage ment, the evaluation of alternatives and the determination of an optimal or at least suboptimal solution is an important but dif?cult task. For most such problems no ef?cient algorithm is known and classical approaches of Operations Research like Mixed Integer Linear Programming or Dynamic Pro gramming are often of limited use due to excessive computation time. Therefore, dedicated heuristic solution approaches have been developed which aim at providing good solutions in reasonable time for a given problem. However, such methods have two major drawbacks: First, they are tailored to a speci?c prob lem and their adaption to other problems is dif?cult and in many cases even impos sible. Second, they are typically designed to "build" one single solution in the most effective way, whereas most decision problems have a vast number of feasible solu tions. Hence usually the chances are high that there exist better ones. To overcome these limitations, problem independent search strategies, in particular metaheuris tics, have been proposed. This book provides an elementary step by step introduction to metaheuristics focusing on the search concepts they are based on. The ?rst part demonstrates un derlying concepts of search strategies using a simple example optimization problem.

The interaction between mathematicians, statisticians and econometricians working in actuarial sciences and finance is producing numerous meaningful scientific results. This volume introduces new ideas, in the form of four-page papers, presented at the international conference Mathematical and Statistical Methods for Actuarial Sciences and Finance (MAF), held at Universidad Carlos III de Madrid (Spain), 4th-6th April 2018. The book covers a wide variety of subjects in actuarial science and financial fields, all discussed in the context of the cooperation between the three quantitative approaches. The topics include: actuarial models; analysis of high frequency financial data; behavioural finance; carbon and green finance; credit risk methods and models; dynamic optimization in finance; financial econometrics; forecasting of dynamical actuarial and financial phenomena; fund performance evaluation; insurance portfolio risk analysis; interest rate models; longevity risk; machine learning and soft-computing in finance; management in insurance business; models and methods for financial time series analysis, models for financial derivatives; multivariate techniques for financial markets analysis; optimization in insurance; pricing; probability in actuarial sciences, insurance and finance; real world finance; risk management; solvency analysis; sovereign risk; static and dynamic portfolio selection and management; trading systems. This book is a valuable resource for academics, PhD students, practitioners, professionals and researchers, and is also of interest to other readers with quantitative background knowledge.

Despite the proliferation of video games in the twenty-first century, the theory of game design is largely underdeveloped, leaving designers on their own to understand what games really are. Helping you produce better games, Game Design Theory: A New Philosophy for Understanding Games presents a bold new path for analyzing and designing games. The author offers a radical yet reasoned way of thinking about games and provides a holistic solution to understanding the difference between games and other types of interactive systems. He clearly details the definitions, concepts, and methods that form the fundamentals of this philosophy. He also uses the philosophy to analyze the history of games and modern trends as well as to design games. Providing a robust, useful philosophy for game design, this book gives you real answers about what games are and how they work. Through this paradigm, you will be better equipped to create fun games.

Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed. The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis.

This edited volume illustrates the connections between machine learning techniques, black box optimization, and no-free lunch theorems. Each of the thirteen contributions focuses on the commonality and interdisciplinary concepts as well as the fundamentals needed to fully comprehend the impact of individual applications and problems. Current theoretical, algorithmic, and practical methods used are provided to stimulate a new effort towards innovative and efficient solutions. The book is intended for beginners who wish to achieve a broad overview of optimization methods and also for more experienced researchers as well as researchers in mathematics, optimization, operations research, quantitative logistics, data analysis, and statistics, who will benefit from access to a quick reference to key topics and methods. The coverage ranges from mathematically rigorous methods to heuristic and evolutionary approaches in an attempt to equip the reader with different viewpoints of the same problem.

The first volume, Geometry, Language and Strategy, extended the concepts of Game Theory, replacing static equilibrium with a deterministic dynamic theory. The first volume opened up many applications that were only briefly touched on. To study the consequences of the deterministic approach in contrast to standard Bayesian approaches, the richness of applications, requires an engineering foundation and discipline, which this volume supplies. It provides a richer list of applications, such as the Prisoner's Dilemma, which extends the resonant behavior of Vol. 1 to more general time-dependent and transient behaviors.

In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains recent developments from singularity theory and semi-algebraic geometry for studying polynomial optimization problems. Classes of generic problems are defined in a simple and elegant manner by using only the two basic (and relatively simple) notions of Newton polyhedron and non-degeneracy conditions associated with a given polynomial optimization problem. These conditions are well known in singularity theory, however, they are rarely considered within the optimization community.Explanations focus on critical points and tangencies of polynomial optimization, Hoelderian error bounds for polynomial systems, Frank-Wolfe-type theorem for polynomial programs and well-posedness in polynomial optimization. It then goes on to look at optimization for the different types of polynomials. Through this text graduate students, PhD students and researchers of mathematics will be provided with the knowledge necessary to use semi-algebraic geometry in optimization.

This book describes the interplay of mechanics, electronics, electrotechnics, automation and biomechanics. It provides a broad overview of mechatronics systems ranging from modeling and dimensional analysis, and an overview of magnetic, electromagnetic and piezo-electric phenomena. It also includes the investigation of the pneumo-fluid-mechanical, as well as electrohydraulic servo systems, modeling of dynamics of an atom/particle embedded in the magnetic field, integrity aspects of the Maxwell's equations, the selected optimization problems of angular velocity control of a DC motor subjected to chaotic disturbances with and without stick-slip dynamics, and the analysis of a human chest adjacent to the elastic backrest aimed at controlling force to minimize relative compression of the chest employing the LQR.This book provides a theoretical background on the analysis of various kinds of mechatronics systems, along with their computational analysis, control, optimization as well as laboratory investigations.

The Greek economic crisis has imperilled the stability of the eurozone, generating much global anxiety. Policymakers, analysts, and the media have daily debated the course of the Greek economy, prescribing ways to move forward. This collection of essays progressively moves from an analysis of the causes of the crisis and the policy responses so far to a debate on some of the country s advantages and capabilities that should underpin its new development model and propel the return to growth. The book analytically chooses to view the glass as half-full and seeks to provide motivation and inspiration for change by indicating some of the economic sectors where Greece maintains a comparative advantage. Therefore, it challenges the emerging picture of Greece as a country doomed to failure, where everything falls apart.

This book presents modern developments in time series econometrics that are applied to macroeconomic and financial time series, bridging the gap between methods and realistic applications. It presents the most important approaches to the analysis of time series, which may be stationary or nonstationary. Modelling and forecasting univariate time series is the starting point. For multiple stationary time series, Granger causality tests and vector autogressive models are presented. As the modelling of nonstationary uni- or multivariate time series is most important for real applied work, unit root and cointegration analysis as well as vector error correction models are a central topic. Tools for analysing nonstationary data are then transferred to the panel framework. Modelling the (multivariate) volatility of financial time series with autogressive conditional heteroskedastic models is also treated.

This book highlights recent developments in multidimensional data visualization, presenting both new methods and modifications on classic techniques. Throughout the book, various applications of multidimensional data visualization are presented including its uses in social sciences (economy, education, politics, psychology), environmetrics, and medicine (ophthalmology, sport medicine, pharmacology, sleep medicine).

The book provides recent research results in optimization-based visualization. Evolutionary algorithms and a two-level optimization method, based on combinatorial optimization and quadratic programming, are analyzed in detail. The performance of these algorithms and the development of parallel versions is discussed.

The encorporation of new visualization techniques to improve the capabilies of artificial neural networks (self-organizing maps, feed-forward networks) is also discussed.

The book includes over 100 detailed images presenting examples of the different visualization techniques that are presented.

This book is intended for scientists and researchers in any field of study where complex and multidimensional data must be represented visually.

Communication Games is a new and radical interpretation of the relationship between culture and communication. It explores the idea that culture and communication studies should be seen predominantly in relation to struggles and conflicts within the social arena. It criticizes the conventional heritage of the social sciences and humanities. Culture and communication are conceived not merely as means of integrating social actors, but as semiotic ways of providing fitness indicators that allow for the resolution of competition between individuals. From the perspective of Peircean semiotics and the Darwinian understanding of life processes, Communication Games redefines culture in terms of Darwin's notion of sexual selection. Moving on from the realization that sexual selection creates individual organisms with conflicting interests, Communication Games emphasizes the contribution of game theory to semiotics and communication studies. The book demonstrates how cooperation and shared conventions eventually emerge, and how conflicts are resolved through the display of costly and inflated signs. It is from these inflated signs and the escalation of excessive messages that cultures gain a certain degree of stability. Communication Games proposes a new way of understanding culture, communication, and semiotic exchange in terms of game theory.

This volume consists of selected essays by participants of the workshop Control at Large Scales: Energy Markets and Responsive Grids held at the Institute for Mathematics and its Applications, Minneapolis, Minnesota, U.S.A. from May 9-13, 2016. The workshop brought together a diverse group of experts to discuss current and future challenges in energy markets and controls, along with potential solutions. The volume includes chapters on significant challenges in the design of markets and incentives, integration of renewable energy and energy storage, risk management and resilience, and distributed and multi-scale optimization and control. Contributors include leading experts from academia and industry in power systems and markets as well as control science and engineering. This volume will be of use to experts and newcomers interested in all aspects of the challenges facing the creation of a more sustainable electricity infrastructure, in areas such as distributed and stochastic optimization and control, stability theory, economics, policy, and financial mathematics, as well as in all aspects of power system operation.

Game theory is a branch of modern applied mathematics that aims to analyse various problems of conflict between parties that have opposed similar or simply different interests.Games are grouped into several classes according to some important features. In Game Theory (2nd Edition), Petrosyan and Zenkevich consider zero-sum two-person games, strategic N-person games in normal form, cooperative games, games in extensive form with complete and incomplete information, differential pursuit games and differential cooperative, and non-cooperative N-person games. The 2nd edition updates heavily from the 1st edition published in 1996.

Combinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research/management science, artificial intelligence, machine learning, and software engineering.Advances in Combinatorial Optimization presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the 'traveling salesman problem' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the 'vertex coloring problem' (VCP)). This work also represents a proof of the equality of the complexity classes 'P' (polynomial time) and 'NP' (nondeterministic polynomial time), and makes a contribution to the theory and application of 'extended formulations' (EFs).On a whole, Advances in Combinatorial Optimization offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.

The Joy of Finite Mathematics: The Language and Art of Math teaches students basic finite mathematics through a foundational understanding of the underlying symbolic language and its many dialects, including logic, set theory, combinatorics (counting), probability, statistics, geometry, algebra, and finance. Through detailed explanations of the concepts, step-by-step procedures, and clearly defined formulae, readers learn to apply math to subjects ranging from reason (logic) to finance (personal budget), making this interactive and engaging book appropriate for non-science, undergraduate students in the liberal arts, social sciences, finance, economics, and other humanities areas. The authors utilize important historical facts, pose interesting and relevant questions, and reference real-world events to challenge, inspire, and motivate students to learn the subject of mathematical thinking and its relevance. The book is based on the authors' experience teaching Liberal Arts Math and other courses to students of various backgrounds and majors, and is also appropriate for preparing students for Florida's CLAST exam or similar core requirements.

"Impulsive Control in Continuous and Discrete-Continuous Systems" is an up-to-date introduction to the theory of impulsive control in nonlinear systems. This is a new branch of the Optimal Control Theory, which is tightly connected to the Theory of Hybrid Systems. The text introduces the reader to the interesting area of optimal control problems with discontinuous solutions, discussing the application of a new and effective method of discontinuous time-transformation. With a large number of examples, illustrations, and applied problems arising in the area of observation control, this book is excellent as a textbook or reference for a senior or graduate-level course on the subject, as well as a reference for researchers in related fields.

Optimization techniques are at the core of data science, including data analysis and machine learning. An understanding of basic optimization techniques and their fundamental properties provides important grounding for students, researchers, and practitioners in these areas. This text covers the fundamentals of optimization algorithms in a compact, self-contained way, focusing on the techniques most relevant to data science. An introductory chapter demonstrates that many standard problems in data science can be formulated as optimization problems. Next, many fundamental methods in optimization are described and analyzed, including: gradient and accelerated gradient methods for unconstrained optimization of smooth (especially convex) functions; the stochastic gradient method, a workhorse algorithm in machine learning; the coordinate descent approach; several key algorithms for constrained optimization problems; algorithms for minimizing nonsmooth functions arising in data science; foundations of the analysis of nonsmooth functions and optimization duality; and the back-propagation approach, relevant to neural networks.

This volume presents selected contributions by top researchers in the field of operations research, originating from the XVI Congress of APDIO. It provides interesting findings and applications of operations research methods and techniques in a wide variety of problems. The contributions address complex real-world problems, including inventory management with lateral transshipments, sectors and routes in solid-waste collection and production planning for perishable food products. It also discusses the latest techniques, making the volume a valuable tool for researchers, students and practitioners who wish to learn about current trends. Of particular interest are the applications of nonlinear and mixed-integer programming, data envelopment analysis, clustering techniques, hybrid heuristics, supply chain management and lot sizing, as well as job scheduling problems. This biennial conference, organized by APDIO, the Portuguese Association of Operational Research, held in Braganca, Portugal, in June 2013, presented a perfect opportunity to discuss the latest development in this field and to narrow the gap between academic researchers and practitioners.

Thanks to recent advancements, optimization is now recognized as a crucial component in research and decision-making across a number of fields. Through optimization, scientists have made tremendous advances in cancer treatment planning, disease control, and drug development, as well as in sequencing DNA, and identifying protein structures. Optimization in Medicine and Biology provides researchers with a comprehensive, single-source reference that will enable them to apply the very latest optimization techniques to their work. With contributions from pioneering international experts this volume integrates strong foundational theory, good modeling techniques, and efficient and robust algorithms with relevant applications Divided into two sections, the first begins with mathematical programming techniques for medical decision making processes and demonstrates their application to optimizing pediatric vaccine formularies, kidney paired donation, and the cost-effectiveness of HIV programs. It also presents recent advances in cancer treatment planning models and solution algorithms, including three-dimensional conventional conformal radiation therapy (3DCRT), intensity modulated radiation therapy (IMRT), tomotherapy, and proton therapy. Part two focuses on optimization in biology and discusses computational algorithms for genomic analysis; probe design and selection, properties of probes, and various algorithms and software packages to aid in probe selection and design. Subsequent chapters introduce a new dihedral angle measure for protein secondary prediction, and an optimization approach for tumor virotherapy with recombinant measles viruses. The editors include a short tutorial appendix on Integer Programming (IP). Highlighting the most recent advances in optimization techniques for solving complex problems in medical research, this book facilitates strong collaborative environments among optimization researchers and medical professionals for future medical research.

The aim of this book is to furnish the reader with a rigorous and detailed exposition of the concept of control parametrization and time scaling transformation. It presents computational solution techniques for a special class of constrained optimal control problems as well as applications to some practical examples. The book may be considered an extension of the 1991 monograph A Unified Computational Approach Optimal Control Problems, by K.L. Teo, C.J. Goh, and K.H. Wong. This publication discusses the development of new theory and computational methods for solving various optimal control problems numerically and in a unified fashion. To keep the book accessible and uniform, it includes those results developed by the authors, their students, and their past and present collaborators. A brief review of methods that are not covered in this exposition, is also included. Knowledge gained from this book may inspire advancement of new techniques to solve complex problems that arise in the future. This book is intended as reference for researchers in mathematics, engineering, and other sciences, graduate students and practitioners who apply optimal control methods in their work. It may be appropriate reading material for a graduate level seminar or as a text for a course in optimal control.

This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.

Game Theory and Exercises introduces the main concepts of game theory, along with interactive exercises to aid readers' learning and understanding. Game theory is used to help players understand decision-making, risk-taking and strategy and the impact that the choices they make have on other players; and how the choices of those players, in turn, influence their own behaviour. So, it is not surprising that game theory is used in politics, economics, law and management. This book covers classic topics of game theory including dominance, Nash equilibrium, backward induction, repeated games, perturbed strategie s, beliefs, perfect equilibrium, Perfect Bayesian equilibrium and replicator dynamics. It also covers recent topics in game theory such as level-k reasoning, best reply matching, regret minimization and quantal responses. This textbook provides many economic applications, namely on auctions and negotiations. It studies original games that are not usually found in other textbooks, including Nim games and traveller's dilemma. The many exercises and the inserts for students throughout the chapters aid the reader's understanding of the concepts. With more than 20 years' teaching experience, Umbhauer's expertise and classroom experience helps students understand what game theory is and how it can be applied to real life examples. This textbook is suitable for both undergraduate and postgraduate students who study game theory, behavioural economics and microeconomics.

With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index

This book features a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in B ethlehem, Pennsylvania, USA between August 16-18, 2017. The conference brought together a diverse group of researchers and practitioners working on both theoretical and practical aspects of continuous and discrete optimization. Topics covered include algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and address the application of deterministic andstochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The selected contributions in this book illustrate the broad diversity of ideas discussed at the meeting.