This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.

The Prisoner's Dilemma is one of the most fiercely debated thought experiments in philosophy and the social sciences, presenting the simple insight that when two or more agents interact, the actions that most benefit each individual may not benefit the group. The fact that when you do what is best for you, and I do what is best for me, we end up in a situation that is worse for both of us makes the Prisoner's Dilemma relevant to a broad range of everyday phenomena. This volume of new essays from leading philosophers, game theorists, and economists examines the ramifications of the Prisoner's Dilemma, the directions in which it continues to lead us, and its links to a variety of topics in philosophy, political science, social science, economics, and evolutionary biology. The volume will be a vital and accessible resource for upper-level students as well as for academic researchers.

This book is devoted to the study of classes of optimal control problems arising in economic growth theory, related to the Robinson-Solow-Srinivasan (RSS) model. The model was introduced in the 1960s by economists Joan Robinson, Robert Solow, and Thirukodikaval Nilakanta Srinivasan and was further studied by Robinson, Nobuo Okishio, and Joseph Stiglitz. Since then, the study of the RSS model has become an important element of economic dynamics. In this book, two large general classes of optimal control problems, both of them containing the RSS model as a particular case, are presented for study. For these two classes, a turnpike theory is developed and the existence of solutions to the corresponding infinite horizon optimal control problems is established. The book contains 9 chapters. Chapter 1 discusses turnpike properties for some optimal control problems that are known in the literature, including problems corresponding to the RSS model. The first class of optimal control problems is studied in Chaps. 2-6. In Chap. 2, infinite horizon optimal control problems with nonautonomous optimality criteria are considered. The utility functions, which determine the optimality criterion, are nonconcave. This class of models contains the RSS model as a particular case. The stability of the turnpike phenomenon of the one-dimensional nonautonomous concave RSS model is analyzed in Chap. 3. The following chapter takes up the study of a class of autonomous nonconcave optimal control problems, a subclass of problems considered in Chap. 2. The equivalence of the turnpike property and the asymptotic turnpike property, as well as the stability of the turnpike phenomenon, is established. Turnpike conditions and the stability of the turnpike phenomenon for nonautonomous problems are examined in Chap. 5, with Chap. 6 devoted to the study of the turnpike properties for the one-dimensional nonautonomous nonconcave RSS model. The utility functions, which determine the optimality criterion, are nonconcave. The class of RSS models is identified with a complete metric space of utility functions. Using the Baire category approach, the turnpike phenomenon is shown to hold for most of the models. Chapter 7 begins the study of the second large class of autonomous optimal control problems, and turnpike conditions are established. The stability of the turnpike phenomenon for this class of problems is investigated further in Chaps. 8 and 9.

With the diversification of Internet services and the increase in mobile users, efficient management of network resources has become an extremely important issue in the field of wireless communication networks (WCNs). Adaptive resource management is an effective tool for improving the economic efficiency of WCN systems as well as network design and construction, especially in view of the surge in mobile device demands. This book presents modelling methods based on queueing theory and Markov processes for a wide variety of WCN systems, as well as precise and approximate analytical solution methods for the numerical evaluation of the system performance. This is the first book to provide an overview of the numerical analyses that can be gleaned by applying queueing theory, traffic theory and other analytical methods to various WCN systems. It also discusses the recent advances in the resource management of WCNs, such as broadband wireless access networks, cognitive radio networks, and green cloud computing. It assumes a basic understanding of computer networks and queueing theory, and familiarity with stochastic processes is also recommended. The analysis methods presented in this book are useful for first-year-graduate or senior computer science and communication engineering students. Providing information on network design and management, performance evaluation, queueing theory, game theory, intelligent optimization, and operations research for researchers and engineers, the book is also a valuable reference resource for students, analysts, managers and anyone in the industry interested in WCN system modelling, performance analysis and numerical evaluation.

DEA is computational at its core and this book will be one of several books that we will look to publish on the computational aspects of DEA. This book by Zhu and Cook will deal with the micro aspects of handling and modeling data issues in modeling DEA problems. DEA's use has grown with its capability of dealing with complex service industry and the public service domain types of problems that require modeling both qualitative and quantitative data. This will be a handbook treatment dealing with specific data problems including the following: (1) imprecise data, (2) inaccurate data, (3) missing data, (4) qualitative data, (5) outliers, (6) undesirable outputs, (7) quality data, (8) statistical analysis, (9) software and other data aspects of modeling complex DEA problems. In addition, the book will demonstrate how to visualize DEA results when the data is more than 3-dimensional, and how to identify efficiency units quickly and accurately.

Constraint Programming is a problem-solving paradigm that establishes a clear distinction between two pivotal aspects of a problem: (1) a precise definition of the constraints that define the problem to be solved and (2) the algorithms and heuristics enabling the selection of decisions to solve the problem. It is because of these capabilities that Constraint Programming is increasingly being employed as a problem-solving tool to solve scheduling problems. Hence the development of Constraint-Based Scheduling as a field of study. The aim of this book is to provide an overview of the most widely used Constraint-Based Scheduling techniques. Following the principles of Constraint Programming, the book consists of three distinct parts: The first chapter introduces the basic principles of Constraint Programming and provides a model of the constraints that are the most often encountered in scheduling problems. Chapters 2, 3, 4, and 5 are focused on the propagation of resource constraints, which usually are responsible for the "hardness" of the scheduling problem. Chapters 6, 7, and 8 are dedicated to the resolution of several scheduling problems. These examples illustrate the use and the practical efficiency of the constraint propagation methods of the previous chapters. They also show that besides constraint propagation, the exploration of the search space must be carefully designed, taking into account specific properties of the considered problem (e.g., dominance relations, symmetries, possible use of decomposition rules). Chapter 9 mentions various extensions of the model and presents promising research directions.

This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers' understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.

This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume."

This handbook aims to serve as a one-stop, reliable source of reference, with curations of survey and expository contributions on the state-of-the-art in Blockchain technology. It covers a comprehensive range of topics, providing the technical and non-technical reader with fundamentals, applications, and deep details on a variety of topics. The readership is expected to span broadly from technologically-minded business professionals and entrepreneurs, to students, instructors, novices and seasoned researchers, in computer science, engineering, software engineering, finance, and data science. Though Blockchain technology is relatively young, its evolution as a field and a practice is booming in growth and its importance to society had never been more important than it is today. Blockchain solutions enable a decentralization of a digital society where people can contribute, collaborate, and transact without having to second-guess the trust and transparency factors with many geographical, financial, and political barriers removed. It is the distributed ledger technology behind the success of Bitcoin, Ethereum, and many emerging applications. The resource is divided into 5 parts. Part 1 (Foundation) walks the reader through a comprehensive set of essential concepts, protocols, and algorithms that lay the foundation for Blockchain. Part 2 (Scalability) focuses on the most pressing challenges of today's blockchain networks in how to keep pace with real-world expectations. Part 3 (Trust and Security) provides detailed coverage on the issues of trust, reputation, and security in Blockchain. Part 4 (Decentralized Finance) is devoted to a high-impact application of Blockchain to finance, the sector that has most benefitted from this technology. Part 5 (Application and Policy) includes several cases where Blockchain applies to the real world.

This is a comprehensive study of various time-dependent scheduling problems in single-, parallel- and dedicated-machine environments. In addition to complexity issues and exact or heuristic algorithms which are typically presented in scheduling books, the author also includes more advanced topics such as matrix methods in time-dependent scheduling, time-dependent scheduling with two criteria and time-dependent two-agent scheduling. The reader should be familiar with the basic notions of calculus, discrete mathematics and combinatorial optimization theory, while the book offers introductory material on theory of algorithms, NP-complete problems, and the basics of scheduling theory. The author includes numerous examples, figures and tables, he presents different classes of algorithms using pseudocode, he completes all chapters with extensive bibliographies, and he closes the book with comprehensive symbol and subject indexes. The previous edition of the book focused on computational complexity of time-dependent scheduling problems. In this edition, the author concentrates on models of time-dependent job processing times and algorithms for solving time-dependent scheduling problems. The book is suitable for researchers working on scheduling, problem complexity, optimization, heuristics and local search algorithms.

This book provides a postgraduate audience the keys they need to understand and further develop a set of tools for the efficient computation of lower bounds and valid inequalities in integer programs and combinatorial optimization problems. After discussing the classical approaches described in the literature, the book addresses how to extend these tools to other non-standard formulations that may be applied to a broad set of applications. Examples are provided to illustrate the underlying concepts and to pave the way for future contributions.

Machine learning heavily relies on optimization algorithms to solve its learning models. Constrained problems constitute a major type of optimization problem, and the alternating direction method of multipliers (ADMM) is a commonly used algorithm to solve constrained problems, especially linearly constrained ones. Written by experts in machine learning and optimization, this is the first book providing a state-of-the-art review on ADMM under various scenarios, including deterministic and convex optimization, nonconvex optimization, stochastic optimization, and distributed optimization. Offering a rich blend of ideas, theories and proofs, the book is up-to-date and self-contained. It is an excellent reference book for users who are seeking a relatively universal algorithm for constrained problems. Graduate students or researchers can read it to grasp the frontiers of ADMM in machine learning in a short period of time.

This book provides energy efficiency quantitative analysis and optimal methods for discrete manufacturing systems from the perspective of global optimization. In order to analyze and optimize energy efficiency for discrete manufacturing systems, it uses real-time access to energy consumption information and models of the energy consumption, and constructs an energy efficiency quantitative index system. Based on the rough set and analytic hierarchy process, it also proposes a principal component quantitative analysis and a combined energy efficiency quantitative analysis. In turn, the book addresses the design and development of quantitative analysis systems. To save energy consumption on the basis of energy efficiency analysis, it presents several optimal control strategies, including one for single-machine equipment, an integrated approach based on RWA-MOPSO, and one for production energy efficiency based on a teaching and learning optimal algorithm. Given its scope, the book offers a valuable guide for students, teachers, engineers and researchers in the field of discrete manufacturing systems.

Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning.

This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.

This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author's lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.

This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

Advances in discrete mathematics are presented in this book with applications in theoretical mathematics and interdisciplinary research. Each chapter presents new methods and techniques by leading experts. Unifying interdisciplinary applications, problems, and approaches of discrete mathematics, this book connects topics in graph theory, combinatorics, number theory, cryptography, dynamical systems, finance, optimization, and game theory. Graduate students and researchers in optimization, mathematics, computer science, economics, and physics will find the wide range of interdisciplinary topics, methods, and applications covered in this book engaging and useful.

This volume comprises a selection of works presented at the Numerical and Evolutionary Optimization (NEO) workshop held in September 2015 in Tijuana, Mexico. The development of powerful search and optimization techniques is of great importance in today's world that requires researchers and practitioners to tackle a growing number of challenging real-world problems. In particular, there are two well-established and widely known fields that are commonly applied in this area: (i) traditional numerical optimization techniques and (ii) comparatively recent bio-inspired heuristics. Both paradigms have their unique strengths and weaknesses, allowing them to solve some challenging problems while still failing in others. The goal of the NEO workshop series is to bring together people from these and related fields to discuss, compare and merge their complimentary perspectives in order to develop fast and reliable hybrid methods that maximize the strengths and minimize the weaknesses of the underlying paradigms. Through this effort, we believe that the NEO can promote the development of new techniques that are applicable to a broader class of problems. Moreover, NEO fosters the understanding and adequate treatment of real-world problems particularly in emerging fields that affect us all such as health care, smart cities, big data, among many others. The extended papers the NEO 2015 that comprise this book make a contribution to this goal.

This tutorial is the first comprehensive introduction to (possibly infinite) linear systems containing strict inequalities and evenly convex sets. The book introduces their application to convex optimization. Particular attention is paid to evenly convex polyhedra and finite linear systems containing strict inequalities. The book also analyzes evenly convex and quasiconvex functions from a conjugacy and duality perspective. It discusses the applications of these functions in economics. Written in an expository style the main concepts and basic results are illustrated with suitable examples and figures..

This book presents the best papers from the 2nd International Conference on Mathematical Research for Blockchain Economy (MARBLE) 2020, 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 focused 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.

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

This book is devoted to a detailed study of the subgradient projection method and its variants for convex optimization problems over the solution sets of common fixed point problems and convex feasibility problems. These optimization problems are investigated to determine good solutions obtained by different versions of the subgradient projection algorithm in the presence of sufficiently small computational errors. The use of selected algorithms is highlighted including the Cimmino type subgradient, the iterative subgradient, and the dynamic string-averaging subgradient. All results presented are new. Optimization problems where the underlying constraints are the solution sets of other problems, frequently occur in applied mathematics. The reader should not miss the section in Chapter 1 which considers some examples arising in the real world applications. The problems discussed have an important impact in optimization theory as well. The book will be useful for researches interested in the optimization theory and its applications.

This book includes selected peer-reviewed papers presented at the International Conference on Modeling, Simulation and Optimization (CoMSO 2021), organized by National Institute of Technology, Silchar, Assam, India, during December 16-18, 2021. The book covers topics of modeling, simulation and optimization, including computational modeling and simulation, system modeling and simulation, device/VLSI modeling and simulation, control theory and applications, modeling and simulation of energy systems and optimization. The book disseminates various models of diverse systems and includes solutions of emerging challenges of diverse scientific fields.

This book offers a timely snapshot of current soft-computing research and solutions to decision-making and optimization problems, which are ubiquitous in the current social and technological context, addressing fields including logistics, transportation and data analysis. Written by leading international experts from the United States, Brazil and Cuba, as well as the United Kingdom, France, Finland and Spain, it discusses theoretical developments in and practical applications of soft computing in fields where these methods are crucial to obtaining better models, including: intelligent transportation systems, maritime logistics, portfolio selection, decision- making, fuzzy cognitive maps, and fault detection. The book is dedicated to Professor Jose L. Verdegay, a pioneer who has been actively pursuing research in fuzzy sets theory and soft computing since 1982, in honor of his 65th birthday.