Optimization and Differentiation is an introduction to the application of optimization control theory to systems described by nonlinear partial differential equations. As well as offering a useful reference work for researchers in these fields, it is also suitable for graduate students of optimal control theory.

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

Practical Financial Optimization is a comprehensive guide to optimization techniques in financial decision making. This book illuminates the relationship between theory and practice, providing the readers with solid foundational knowledge.* Focuses on classical static mean-variance analysis and portfolio immunization, scenario-based models, multi-period dynamic portfolio optimization, and the relationships between classes of models* Analyizes real world applications and implications for financial engineers* Includes a list of models and a section on notations that includes a glossary of symbols and abbreviations

The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

This English version of Ruslan L. Stratonovich's Theory of Information (1975) builds on theory and provides methods, techniques, and concepts toward utilizing critical applications. Unifying theories of information, optimization, and statistical physics, the value of information theory has gained recognition in data science, machine learning, and artificial intelligence. With the emergence of a data-driven economy, progress in machine learning, artificial intelligence algorithms, and increased computational resources, the need for comprehending information is essential. This book is even more relevant today than when it was first published in 1975. It extends the classic work of R.L. Stratonovich, one of the original developers of the symmetrized version of stochastic calculus and filtering theory, to name just two topics. Each chapter begins with basic, fundamental ideas, supported by clear examples; the material then advances to great detail and depth. The reader is not required to be familiar with the more difficult and specific material. Rather, the treasure trove of examples of stochastic processes and problems makes this book accessible to a wide readership of researchers, postgraduates, and undergraduate students in mathematics, engineering, physics and computer science who are specializing in information theory, data analysis, or machine learning.

Many systems architecture optimization problems are characterized by a variable number of optimization variables. Many classical optimization algorithms are not suitable for such problems. The book presents recently developed optimization concepts that are designed to solve such problems. These new concepts are implemented using genetic algorithms and differential evolution. The examples and applications presented show the effectiveness of the use of these new algorithms in optimizing systems architectures. The book focuses on systems architecture optimization. It covers new algorithms and its applications, besides reviewing fundamental mathematical concepts and classical optimization methods. It also provides detailed modeling of sample engineering problems. The book is suitable for graduate engineering students and engineers. The second part of the book includes numerical examples on classical optimization algorithms, which are useful for undergraduate engineering students. While focusing on the algorithms and their implementation, the applications in this book cover the space trajectory optimization problem, the optimization of earth orbiting satellites orbits, and the optimization of the wave energy converter dynamic system: architecture and control. These applications are illustrated in the starting of the book, and are used as case studies in later chapters for the optimization methods presented in the book.

This open access book serves as a compact source of information on sine cosine algorithm (SCA) and a foundation for developing and advancing SCA and its applications. SCA is an easy, user-friendly, and strong candidate in the field of metaheuristics algorithms. Despite being a relatively new metaheuristic algorithm, it has achieved widespread acceptance among researchers due to its easy implementation and robust optimization capabilities. Its effectiveness and advantages have been demonstrated in various applications ranging from machine learning, engineering design, and wireless sensor network to environmental modeling. The book provides a comprehensive account of the SCA, including details of the underlying ideas, the modified versions, various applications, and a working MATLAB code for the basic SCA.

As power and gas markets are becoming more and more mature and globally competitive, the importance of reaching maximum potential economic efficiency is fundamental in all the sectors of the value chain, from investments selection to asset optimization, trading and sales. Optimization techniques can be used in many different fields of the energy industry, in order to reduce production and financial costs, increase sales revenues and mitigate all kinds of risks potentially affecting the economic margin. For this reason the industry has now focused its attention on the general concept of optimization and to the different techniques (mainly mathematical techniques) to reach it. Optimization Methods for Gas and Power Markets presents both theoretical elements and practical examples for solving energy optimization issues in gas and power markets. Starting with the theoretical framework and the basic business and economics of power and gas optimization, it quickly moves on to review the mathematical optimization problems inherent to the industry, and their solutions - all supported with examples from the energy sector. Coverage ranges from very long-term (and capital intensive) optimization problems such as investment valuation/diversification to asset (gas and power) optimization/hedging problems, and pure trading decisions. This book first presents the readers with various examples of optimization problems arising in power and gas markets, then deals with general optimization problems and describes the mathematical tools useful for their solution. The remainder of the book is dedicated to presenting a number of key business cases which apply the proposed techniques to concrete market problems. Topics include static asset optimization, real option evaluation, dynamic optimization of structured products like swing, virtual storage or virtual power plant contracts and optimal trading in intra-day power markets. As the book progresses, so too does the level of mathematical complexity, providing readers with an appreciation of the growing sophistication of even common problems in current market practice. Optimization Methods for Gas and Power Markets provides a valuable quantitative guide to the technicalities of optimization methodologies in gas and power markets; it is essential reading for practitioners in the energy industry and financial sector who work in trading, quantitative analysis and energy risk modeling.

This book gives a detailed information of various real-life applications from various fields using nature inspired optimization techniques. These techniques are proven to be efficient and robust in many difficult problems in literature. The authors provide detailed information about real-life problems and how various nature inspired optimizations are applied to solve these problems. The authors discuss techniques such as Biogeography Based Optimization, Glow Swarm Optimization, Elephant herd Optimization Algorithm, Cuckoo Search Algorithm, Ant Colony Optimization, and Grey Wolf Optimization etc. These algorithms are applied to a wide range of problems from the field of engineering, finance, medicinal etc. As an important part of the Women in Science and Engineering book series, the work highlights the contribution of women leaders in nature inspired optimization, inspiring women and men, girls and boys to enter and apply themselves to the field.

How do you fly an airplane from one point to another as fast as possible? What is the best way to administer a vaccine to fight the harmful effects of disease? What is the most efficient way to produce a chemical substance? This book presents practical methods for solving real optimal control problems such as these. This third edition focuses on the direct transcription method for optimal control, and features: A summary of relevant material in constrained optimization, including nonlinear programming. Discretization techniques appropriate for ordinary differential equations and differential-algebraic equations. Several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy. The third edition has been thoroughly updated and includes: New material on implicit Runge-Kutta discretization techniques. New chapters on partial differential equations and delay equations. More than 70 test problems and open source FORTRAN code for all of the problems. This book will be valuable for academic and industrial research and development in optimal control theory and applications. It is appropriate as a primary or supplementary text for advanced undergraduate and graduate students.

A fun and stunningly illustrated introduction to the art of linear optimization Linear optimization is a powerful modeling method for discovering the best solution to a problem among a set of available alternatives. It is one of today's most important branches of mathematics and computer science-and also a surprisingly rich medium for creating breathtaking works of art. Opt Art takes readers on an entertaining tour of linear optimization and its applications, showing along the way how it can be used to design visual art. Robert Bosch provides a lively and accessible introduction to the geometric, algebraic, and algorithmic foundations of optimization. He presents classical applications, such as the legendary Traveling Salesman Problem, and shows how to adapt them to make optimization art-opt art. Each chapter in this marvelously illustrated book begins with a problem or puzzle and demonstrates how the solution can be derived using a host of artistic methods and media, including 3D printing, laser cutting, and computer-controlled machining. Bosch focuses on mathematical modeling throughout-converting a problem into a workable mathematical form, solving it using optimization techniques, and examining the results, which can take the form of mosaics, line drawings, and even sculpture. All you need is some high-school algebra, geometry, and calculus to follow along. Featuring more than a hundred illustrations and photos of Bosch's own art, Opt Art demonstrates how mathematics and computing can be used to create beauty and express emotion through amazing works of art.

This edited volume is an in-depth collation of the usage of different quantitative decision making techniques in practical areas such as lean & green supply chain, reverse logistics, perishable logistics, closed loop supply chain, sustainable project management, retail management, block chain applications, optimal supplier selection problem, demand/supply modelling, forecasting under uncertainties, scheduling & sequencing, resource constraint logistics, dynamic network supply chain, risk evaluation, and so on. Additionally, the book also solves these issues in theoretical and practical context using innovative mathematical tools. Consisting of selected papers from the 23rd Annual International Conference of the Society of Operations Management, this book's highlight is not only the coverage of interesting topics, but also how these topics are dealt with, such that post-graduate students as well as researchers and industry personnel working in areas like engineering, economics, social sciences, management, mathematics, etc., can derive the maximum benefit by reading or referring to this book. Apart from the emphasis on new mathematical, operations research, operations management, and statistical techniques, the authors also ensure that all the concepts are made clear by highlighting their practical significance in different areas of applications of operations management. By using novel presentation methods, the book offers a good practical flavor of all the different topics relevant to operations management in the coming decades.

This book presents techniques for determining uncertainties in numerical solutions with applications in the fields of business administration, civil engineering, and economics, using Excel as a computational tool. Also included are solutions to uncertainty problems involving stochastic methods. The list of topics specially covered in this volume includes linear and nonlinear programming, Lagrange multipliers (for sensitivity), multi objective optimization, and Game Theory, as well as linear algebraic equations, and probability and statistics. The book also provides a selection of numerical methods developed for Excel, in order to enhance readers' understanding. As such, it offers a valuable guide for all graduate and undergraduate students in the fields of economics, business administration, civil engineering, and others that rely on Excel as a research tool.

Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

Optimization methods play a central role in financial modeling. This textbook is devoted to explaining how state-of-the-art optimization theory, algorithms, and software can be used to efficiently solve problems in computational finance. It discusses some classical mean-variance portfolio optimization models as well as more modern developments such as models for optimal trade execution and dynamic portfolio allocation with transaction costs and taxes. Chapters discussing the theory and efficient solution methods for the main classes of optimization problems alternate with chapters discussing their use in the modeling and solution of central problems in mathematical finance. This book will be interesting and useful for students, academics, and practitioners with a background in mathematics, operations research, or financial engineering. The second edition includes new examples and exercises as well as a more detailed discussion of mean-variance optimization, multi-period models, and additional material to highlight the relevance to finance.

This book is a collection of high-quality research papers presented at the International Conference on Smart and Intelligent Systems (SIS 2021), which will be held in Velagapudi Ramakrishna Siddhartha Engineering College (VRSEC), Andhra Pradesh, India, during February 25-26, 2021, in virtual mode. It highlights how recent informatics intelligent systems have successfully been used to develop innovative smart techniques and infrastructure in the field of modern engineering and technology. The book will also be of interest to those working in the field of computational intelligence, smart computer network and security analysis, control and automation system, cloud computing, fog computing and IoT, smart grid communication, smart cities, solar cell synthesis and their performance, green technology, and many more. The contents of this book prove useful to researchers and professionals.

This edited book addresses the challenges in managing the operations and supply chain of organizations in the era of internet of things and Industry 4.0. It presents cutting edge research on real world operations related problems, in-depth analyses, and relevant managerial implications. Wide variety of solution approaches such as quantitative, quantitative, and simulations are presented in the context of managing the operations and supply chains. Consisting of selected papers from the XXIII Annual International Conference of Society of Operations Management, this volume is part of a two volume series with the other book consisting of chapters on quantitative decision making. This edited book covers various quantitative models on operations and supply chain management such as inventory optimization, machine learning-operations research integrated model for healthcare systems, game-theoretic analysis of review strategies in truthful information sharing, design of contracts in supply chains, supply chain optimization, inventory routing, and shop floor scheduling. In addition to the quantitative models, several innovative heuristics are proposed for different problems. This book explores qualitative models on improving the performance of small and medium enterprises and petroleum industries and a simulation model for staff allocation in the information technology industry. Finally, this book provides review articles on vaccine supply chains and behavioral operations management. The book throws light on the emerging trends in the use of analytics, optimization, and simulation tools and empirical analysis to improve the performance of operations and supply chains of organizations. It will serve as an essential resource for practitioners, students, faculty members and scholars in operations management and related areas to gain knowledge and pursue high quality research on developments in areas such as managing the resource management and the solution methodology---innovative tools employed in addressing the real world problems and the different optimization techniques.

This book is one-stop shop which offers essential information one must know and can implement in real-time business expansions to solve engineering problems in various disciplines. It will also help us to make future predictions and decisions using AI algorithms for engineering problems. Machine learning and optimizing techniques provide strong insights into novice users. In the era of big data, there is a need to deal with data science problems in multidisciplinary perspective. In the real world, data comes from various use cases, and there is a need of source specific data science models. Information is drawn from various platforms, channels, and sectors including web-based media, online business locales, medical services studies, and Internet. To understand the trends in the market, data science can take us through various scenarios. It takes help of artificial intelligence and machine learning techniques to design and optimize the algorithms. Big data modelling and visualization techniques of collected data play a vital role in the field of data science. This book targets the researchers from areas of artificial intelligence, machine learning, data science and big data analytics to look for new techniques in business analytics and applications of artificial intelligence in recent businesses.

The overall structure of this new edition is three-tier: Part I presents the basics, Part II is concerned with methodological issues, and Part III discusses advanced topics. In the second edition the authors have reorganized the material to focus on problems, how to represent them, and then how to choose and design algorithms for different representations. They also added a chapter on problems, reflecting the overall book focus on problem-solvers, a chapter on parameter tuning, which they combined with the parameter control and "how-to" chapters into a methodological part, and finally a chapter on evolutionary robotics with an outlook on possible exciting developments in this field. The book is suitable for undergraduate and graduate courses in artificial intelligence and computational intelligence, and for self-study by practitioners and researchers engaged with all aspects of bioinspired design and optimization.

Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? This question has preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer. This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals how the idea has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition - one that will be essential reading for popular-science buffs and historians of science alike.

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 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.

For students in industrial and systems engineering (ISE) and operations research (OR) to understand optimization at an advanced level, they must first grasp the analysis of algorithms, computational complexity, and other concepts and modern developments in numerical methods. Satisfying this prerequisite, Numerical Methods and Optimization: An Introduction combines the materials from introductory numerical methods and introductory optimization courses into a single text. This classroom-tested approach enriches a standard numerical methods syllabus with optional chapters on numerical optimization and provides a valuable numerical methods background for students taking an introductory OR or optimization course.

The first part of the text introduces the necessary mathematical background, the digital representation of numbers, and different types of errors associated with numerical methods. The second part explains how to solve typical problems using numerical methods. Focusing on optimization methods, the final part presents basic theory and algorithms for linear and nonlinear optimization.

The book assumes minimal prior knowledge of the topics. Taking a rigorous yet accessible approach to the material, it includes some mathematical proofs as samples of rigorous analysis but in most cases, uses only examples to illustrate the concepts. While the authors provide a MATLAB(r) guide and code available for download, the book can be used with other software packages.

The Subject A little explanation is in order for our choice of the title Linear Opti- 1 mization (and corresponding terminology) for what has traditionally been called Linear Programming.Theword programming in this context can be confusing and/or misleading to students. Linear programming problems are referred to as optimization problems but the general term linear p- gramming remains. This can cause people unfamiliar with the subject to think that it is about programming in the sense of writing computer code. It isn't. This workbook is about the beautiful mathematics underlying the ideas of optimizing linear functions subject to linear constraints and the algorithms to solve such problems. In particular, much of what we d- cuss is the mathematics of Simplex Algorithm for solving such problems, developed by George Dantzig in the late 1940s. The word program in linear programming is a historical artifact. When Dantzig ?rstdevelopedthe Simplex Algorithm to solvewhat arenowcalled linear programming problems, his initial model was a class of resource - location problems to be solved for the U.S. Air Force. The decisions about theallocationswerecalled'Programs'bytheAirForce, andhencetheterm.

Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION

"This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list."—Optima

"A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for understanding the structure of and solving the resulting integer programming problems."—Computing Reviews

"[This book] can serve as a basis for various graduate courses on discrete optimization as well as a reference book for researchers and practitioners."—Mathematical Reviews

"This comprehensive and wide-ranging book will undoubtedly become a standard reference book for all those in the field of combinatorial optimization."—Bulletin of the London Mathematical Society

"This text should be required reading for anybody who intends to do research in this area or even just to keep abreast of developments."—Times Higher Education Supplement, London

Also of interest . . .

INTEGER PROGRAMMING Laurence A. Wolsey Comprehensive and self-contained, this intermediate-level guide to integer programming provides readers with clear, up-to-date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively. 1998 (0-471-28366-5) 260 pp.