This book examines the main methodological and theoretical developments in stochastic global optimization. It is designed to inspire readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods. Among the book's features is a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms.

This proceedings volume, the fifth in a series from the Combinatorial and Additive Number Theory (CANT) conferences, is based on talks from the 19th annual workshop, held online due to the COVID-19 pandemic. Organized every year since 2003 by the New York Number Theory Seminar at the CUNY Graduate Center, the workshops survey state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. The CANT 2021 meeting featured over a hundred speakers from North and South America, Europe, Asia, Australia, and New Zealand, and was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain peer-reviewed and edited papers on current topics in number theory. Topics featured in this volume include sumsets, minimal bases, Sidon sets, analytic and prime number theory, combinatorial and discrete geometry, numerical semigroups, and a survey of expansion, divisibility, and parity. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

Variational principles have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an idea which came to be a cornerstone of geometrical optics. This book explains variational principles and charts their use throughout modern physics. It examines the analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. The book also offers simple but rich first impressions of Einstein’s General Relativity, Feynman’s Quantum Mechanics, and more that reveal amazing interconnections between various fields of physics.

The field of global optimization has been developing at a rapid pace. There is a journal devoted to the topic, as well as many publications and notable books discussing various aspects of global optimization. This book is intended to complement these other publications with a focus on stochastic methods for global optimization. Stochastic methods, such as simulated annealing and genetic algo rithms, are gaining in popularity among practitioners and engineers be they are relatively easy to program on a computer and may be cause applied to a broad class of global optimization problems. However, the theoretical performance of these stochastic methods is not well under stood. In this book, an attempt is made to describe the theoretical prop erties of several stochastic adaptive search methods. Such a theoretical understanding may allow us to better predict algorithm performance and ultimately design new and improved algorithms. This book consolidates a collection of papers on the analysis and de velopment of stochastic adaptive search. The first chapter introduces random search algorithms. Chapters 2-5 describe the theoretical anal ysis of a progression of algorithms. A main result is that the expected number of iterations for pure adaptive search is linear in dimension for a class of Lipschitz global optimization problems. Chapter 6 discusses algorithms, based on the Hit-and-Run sampling method, that have been developed to approximate the ideal performance of pure random search. The final chapter discusses several applications in engineering that use stochastic adaptive search methods."

In this chapter the topic of this book is introduced. Section 1. 1 provides a brief and rather general motivation for the scientific project undertaken here. Interest groups are a very popular object of scientific inquiry, and they received already considerable research attention from scholars in political science, as well as from researchers in economics. Necessarily, then, this book adds to a literature which is already quite developed. A detailed positioning in this literature of the theoretical material presented in this monograph will be given in Chapter 2. This second chapter will also, by means of a review of the empirical literature, provide a more general overview of the issues deemed to be important when studying the influence of interest groups on public policy. The outline of the entire book is described in greater detail in Section 1. 2. As most issues involved are more easily presented in later chapters, this introductory chapter is kept brief. 1. 1 MOTIVATION Substantial political power is often attributed to interest groups. Examples abound in both the economics and political science literature, as well as in journalistic accounts and popular publications. On many occasions the authors express concerns about the negative impact of interest groups on the democratic quality of government. "The interests of a small group are served at the expense of the interests of the general public, the taxpayers ," is an often heard popular complaint.

This Festschrift is dedicated to Goetz Trenkler on the occasion of his 65th birthday. As can be seen from the long list of contributions, Goetz has had and still has an enormous range of interests, and colleagues to share these interests with. He is a leading expert in linear models with a particular focus on matrix algebra in its relation to statistics. He has published in almost all major statistics and matrix theory journals. His research activities also include other areas (like nonparametrics, statistics and sports, combination of forecasts and magic squares, just to mention afew). Goetz Trenkler was born in Dresden in 1943. After his school years in East G- many and West-Berlin, he obtained a Diploma in Mathematics from Free University of Berlin (1970), where he also discovered his interest in Mathematical Statistics. In 1973, he completed his Ph.D. with a thesis titled: On a distance-generating fu- tion of probability measures. He then moved on to the University of Hannover to become Lecturer and to write a habilitation-thesis (submitted 1979) on alternatives to the Ordinary Least Squares estimator in the Linear Regression Model, a topic that would become his predominant ?eld of research in the years to come.

The scope of this volume is primarily to analyze from different methodological perspectives similar valuation and optimization problems arising in financial applications, aimed at facilitating a theoretical and computational integration between methods largely regarded as alternatives. Increasingly in recent years, financial management problems such as strategic asset allocation, asset-liability management, as well as asset pricing problems, have been presented in the literature adopting formulation and solution approaches rooted in stochastic programming, robust optimization, stochastic dynamic programming (including approximate SDP) methods, as well as policy rule optimization, heuristic approaches and others. The aim of the volume is to facilitate the comprehension of the modeling and methodological potentials of those methods, thus their common assumptions and peculiarities, relying on similar financial problems. The volume will address different valuation problems common in finance related to: asset pricing, optimal portfolio management, risk measurement, risk control and asset-liability management.The volume features chapters of theoretical and practical relevance clarifying recent advances in the associated applied field from different standpoints, relying on similar valuation problems and, as mentioned, facilitating a mutual and beneficial methodological and theoretical knowledge transfer. The distinctive aspects of the volume can be summarized as follows: Strong benchmarking philosophy, with contributors explicitly asked to underline current limits and desirable developments in their areas. Theoretical contributions, aimed at advancing the state-of-the-art in the given domain with a clear potential for applications The inclusion of an algorithmic-computational discussion of issues arising on similar valuation problems across different methods. Variety of applications: rarely is it possible within a single volume to consider and analyze different, and possibly competing, alternative optimization techniques applied to well-identified financial valuation problems. Clear definition of the current state-of-the-art in each methodological and applied area to facilitate future research directions.

There are many examples of cooperation in Nature: cells cooperate to form tissues, organs cooperate to form living organisms, and individuals cooperate to raise their offspring or to hunt. However, why cooperation emerges and survives in hostile environments, when defecting would be a much more profitable short-term strategy, is a question that still remains open. During the past few years, several explanations have been proposed, including kin and group selection, punishment and reputation mechanisms, or network reciprocity. This last one will be the center of the present study. The thesis explores the interface between the underlying structure of a given population and the outcome of the cooperative dynamics taking place on top of it, (namely, the Prisoner's Dilemma Game). The first part of this work analyzes the case of a static system, where the pattern of connections is fixed, so it does not evolve over time. The second part develops two models for growing topologies, where the growth and the dynamics are entangled.

Operations research and mathematical programming would not be as advanced today without the many advances in interior point methods during the last decade. These methods can now solve very efficiently and robustly large scale linear, nonlinear and combinatorial optimization problems that arise in various practical applications. The main ideas underlying interior point methods have influenced virtually all areas of mathematical programming including: analyzing and solving linear and nonlinear programming problems, sensitivity analysis, complexity analysis, the analysis of Newton's method, decomposition methods, polynomial approximation for combinatorial problems etc. This book covers the implications of interior techniques for the entire field of mathematical programming, bringing together many results in a uniform and coherent way. For the topics mentioned above the book provides theoretical as well as computational results, explains the intuition behind the main ideas, gives examples as well as proofs, and contains an extensive up-to-date bibliography. Audience: The book is intended for students, researchers and practitioners with a background in operations research, mathematics, mathematical programming, or statistics.

This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily di erentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of di erent problems arising in the eld. It is organized into three parts:

1. convex and nonconvex analysis and the theory of NSO;

2. test problems and practical applications;

3. a guide to NSO software.The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the eld, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization."

This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. The author demonstrates how this method can be utilized as a convenient tool for proving the existence of these solutions when others may fail, such as in cases of evolution equations with nonautonomous operators, with low regular data, or with singular diffusion coefficients. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation. This procedure simplifies the proof of the existence of minimizers and, in particular, the determination of the first-order conditions of optimality. The dual variational formulation is illustrated in the text with specific diffusion equations that have general nonlinearities provided by potentials having various stronger or weaker properties. These equations can represent mathematical models to various real-world physical processes. Inverse problems and optimal control problems are also considered, as this technique is useful in their treatment as well.

This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 16th Symposium of the International Society of Dynamic Games, held July 9-12, 2014, in Amsterdam. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including differential games, evolutionary games, and stochastic games. They discuss theoretical developments, algorithmic methods, issues relating to lack of information, and applications in areas such as biological or economical competition, stability in communication networks, and maintenance decisions in an electricity market, just to name a few. Advances in Dynamic and Evolutionary Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinary audience of researchers, practitioners, and advanced graduate students.

This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate the theory, like population equations, neutron transport theory, delay equations or flows in networks. Each chapter is accompanied by a large set of exercises. An up-to-date bibliography and a detailed subject index help the interested reader. The book is intended primarily for graduate and master students. The finite dimensional part, however, can be followed by an advanced bachelor with a solid knowledge of linear algebra and calculus.

This text provides the undergraduate chemical engineering student with the necessary tools for problem solving in chemical or bio-engineering processes. In a friendly, simple, and unified framework, the exposition aptly balances theory and practice. It uses minimal mathematical concepts, terms, algorithms, and describes the main aspects of chemical process optimization using MATLAB and GAMS. Numerous examples and case studies are designed for students to understand basic principles of each optimization method and elicit the immediate discovery of practical applications. Problem sets are directly tied to real-world situations most commonly encountered in chemical engineering applications. Chapters are structured with handy learning summaries, terms and concepts, and problem sets, and individually reinforce the basics of particular optimization methods. Additionally, the wide breadth of topics that may be encountered in courses such as Chemical Process Optimization, Chemical Process Engineering, Optimization of Chemical Processes, are covered in this accessible text. The book provides formal introductions to MATLAB, GAMS, and a revisit to pertinent aspects of undergraduate calculus. While created for coursework, this text is also suitable for independent study. A full solutions manual is available to instructors who adopt the text for their course.

This book is a rigorous but practical presentation of the techniques of uncertainty quantification, with applications in R and Python. This volume includes mathematical arguments at the level necessary to make the presentation rigorous and the assumptions clearly established, while maintaining a focus on practical applications of uncertainty quantification methods. Practical aspects of applied probability are also discussed, making the content accessible to students. The introduction of R and Python allows the reader to solve more complex problems involving a more significant number of variables. Users will be able to use examples laid out in the text to solve medium-sized problems. The list of topics covered in this volume includes linear and nonlinear programming, Lagrange multipliers (for sensitivity), multi-objective optimization, game theory, as well as linear algebraic equations, and probability and statistics. Blending theoretical rigor and practical applications, this volume will be of interest to professionals, researchers, graduate and undergraduate students interested in the use of uncertainty quantification techniques within the framework of operations research and mathematical programming, for applications in management and planning.

Models and Experiments in Risk and Rationality presents original contributions to the areas of individual choice, experimental economics, operations and analysis, multiple criteria decision making, market uncertainty, game theory and social choice. The papers, which were presented at the FUR VI conference, are arranged to appear in order of increasing complexity of the decision environment or social context in which they situate themselves. The first section Psychological Aspects of Risk-Bearing', considers choice at the purely individual level and for the most part, free of any specific economic or social context. The second section examines individual choice within the classical expected utility approach while the third section works from a perspective that includes non-expected utility preferences over lotteries. Section four, Multiple Criteria Decision-Making Under Uncertainty', considers the more specialized but crucial context of uncertain choice involving tradeoffs between competing criteria -- a field which is becoming of increasing importance in applied decision analysis. The final two sections examine uncertain choice in social or group contexts.

The author of this book made an attempt to create the general theory of optimization of linear systems (both distributed and lumped) with a singular control. The book touches upon a wide range of issues such as solvability of boundary values problems for partial differential equations with generalized right-hand sides, the existence of optimal controls, the necessary conditions of optimality, the controllability of systems, numerical methods of approximation of generalized solutions of initial boundary value problems with generalized data, and numerical methods for approximation of optimal controls. In particular, the problems of optimization of linear systems with lumped controls (pulse, point, pointwise, mobile and so on) are investigated in detail.

Contains case studies from engineering and operations research

Includes commented literature for each chapter

This volume highlights contributions of women mathematicians in the study of complex materials and includes both original research papers and reviews. The featured topics and methods draw on the fields of Calculus of Variations, Partial Differential Equations, Functional Analysis, Differential Geometry and Topology, as well as Numerical Analysis and Mathematical Modelling. Areas of applications include foams, fluid-solid interactions, liquid crystals, shape-memory alloys, magnetic suspensions, failure in solids, plasticity, viscoelasticity, homogenization, crystallization, grain growth, and phase-field models.

The research of Antanas Zilinskas has focused on developing models for global optimization, implementing and investigating the corresponding algorithms, and applying those algorithms to practical problems. This volume, dedicated to Professor Zilinskas on the occasion of his 60th birthday, contains new survey papers in which leading researchers from the field present various models and algorithms for solving global optimization problems.

This volume provides updated, in-depth material on the application of intelligent optimization in biology and medicine. The aim of the book is to present solutions to the challenges and problems facing biology and medicine applications. This Volume comprises of 13 chapters, including an overview chapter, providing an up-to-date and state-of-the research on the application of intelligent optimization for bioinformatics applications, DNA based Steganography, a modified Particle Swarm Optimization Algorithm for Solving Capacitated Maximal Covering Location Problem in Healthcare Systems, Optimization Methods for Medical Image Super Resolution Reconstruction and breast cancer classification. Moreover, some chapters that describe several bio-inspired approaches in MEDLINE Text Mining, DNA-Binding Proteins and Classes, Optimized Tumor Breast Cancer Classification using Combining Random Subspace and Static Classifiers Selection Paradigms, and Dental Image Registration. The book will be a useful compendium for a broad range of readers-from students of undergraduate to postgraduate levels and also for researchers, professionals, etc.-who wish to enrich their knowledge on Intelligent Optimization in Biology and Medicine and applications with one single book.

This book presents the best papers from the 3rd International Conference on Mathematical Research for Blockchain Economy (MARBLE) 2022, held in Vilamoura, Portugal. While most blockchain conferences and forums are dedicated to business applications, product development or Initial Coin Offering (ICO) launches, this conference focuses on the mathematics behind blockchain to bridge the gap between practice and theory. Blockchain Technology has been considered as the most fundamental and revolutionising invention since the Internet. Every year, thousands of blockchain projects are launched and circulated in the market, and there is a tremendous wealth of blockchain applications, from finance to healthcare, education, media, logistics and more. However, due to theoretical and technical barriers, most of these applications are impractical for use in a real-world business context. The papers in this book reveal the challenges and limitations, such as scalability, latency, privacy and security, and showcase solutions and developments to overcome them.

The aim of Metaheuristics: Progress in Complex Systems Optimization is to provide several different kinds of information: a delineation of general metaheuristics methods, a number of state-of-the-art articles from a variety of well-known classical application areas as well as an outlook to modern computational methods in promising new areas. Therefore, this book may equally serve as a textbook in graduate courses for students, as a reference book for people interested in engineering or social sciences, and as a collection of new and promising avenues for researchers working in this field. Highlighted are recent developments in the areas of Simulated Annealing, Path Relinking, Scatter Search, Tabu Search, Variable Neighborhood Search, Hyper-heuristics, Constraint Programming, Iterated Local Search, GRASP, bio-inspired algorithms like Genetic Algorithms, Memetic Algorithms, Ant Colony Optimization or Swarm Intelligence, and several other paradigms.

This book presents the development of an optimization platform for geotechnical engineering, which is one of the key components in smart geotechnics. The book discusses the fundamentals of the optimization algorithm with constitutive models of soils. Helping readers easily understand the optimization algorithm applied in geotechnical engineering, this book first introduces the methodology of the optimization-based parameter identification, and then elaborates the principle of three newly developed efficient optimization algorithms, followed by the ideas of a variety of laboratory tests and formulations of constitutive models. Moving on to the application of optimization methods in geotechnical engineering, this book presents an optimization-based parameter identification platform with a practical and concise interface based on the above theories. The book is intended for undergraduate and graduate-level teaching in soil mechanics and geotechnical engineering and other related engineering specialties. It is also of use to industry practitioners, due to the inclusion of real-world applications, opening the door to advanced courses on both modeling and algorithm development within the industrial engineering and operations research fields.

Why do some games seem to be universal while others have a particular connection to the culture of the people playing them? Around the World in 80 Games is about the mathematics of chance, game theory, gamification, gaming strategies and computer games. Traversing the globe, Marcus du Sautoy looks at the genesis of games new and old, explores how to invent a good game and explains the fascination of a popular lockdown game. The most simple games endure: board games, card games and dice games have captivated us for centuries and the acclaimed mathematician and author of The Creativity Code (among many others) will once again bring mathematics to the fore with insight and aplomb in Around the World in 80 Games.