Optimering

Optimering är en komplett grundbok i optimeringslära som passar för både enklare och mer avancerade kurser på universitetsnivå.

Läsaren får en mångsidig verktygslåda för att lösa praktiska optimeringsproblem. Fokus ligger på användbara metoder snarare än teori.

Andra utmärkande drag:

Täcker alla delar av optimeringens grunder Är ovanligt grundlig i behandlingen av kombinatorisk optimering och optimering av grafer Innehåller en stor mängd övningsuppgifter, tillräckligt för både lärarledda lektioner och hemuppgifter

Språket är enkelt och beskrivningarna inleds genomgående med exempel där författaren konkret förklarar när och hur metoderna kan användas.

Om författarnaFörfattaren Kaj Holmberg är professor i optimeringslära vid Linköpings universitet och aktiv forskare. Han har undervisat i ämnet i över 30 år och nominerats till Linköpings teknologers studentkårs pris för bästa pedagog.

This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material is accessible to readers with knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics

Linjär programmering brukar ses som en relativt lättillgänglig del av optimeringsläran. Syftet med denna bok är att göra linjär programm­ering ännu mer lättillgängligt genom att fokusera på ­tillämpning. Utgångspunkten är att man vid i stort sett all praktisk tillämpning ­använder datorstöd för att lösa linjära optimeringsmodeller, men att man själv måste kunna formulera modeller för specifika besluts­problem. Det innebär att en praktiker har betydligt större nytta av ­kunskaper i modellbygge än kunskaper om lösningsalgoritmer och annan bakomliggande matematisk teori.Det här är alltså inte i första hand en bok i optimeringslära, utan ­snarare en bok om beslutsmodeller där element från optimeringsläran tillämpas. Inför denna andra upplaga av boken har de flesta kapitel uppdaterats. Dessutom har ett nytt kapitel om absolutvärden och två nya kapitel om stokastisk programmering tillkommit. Boken är avsedd att kunna användas både som kurslitteratur på ­universitets- och högskolenivå samt som verktygslåda för praktiker.

Elementär optimeringslära är ett grundläggande komplement till avancerade böcker inom optimeringslära. I boken läggs stor vikt vid att i lagom takt introducera läsaren till den teori och de tekniker som behövs inom grundläggande optimeringslära. Boken innehåller över 200 lösta exempel och mer än 400 övningsuppgifter med svar.Elementär optimeringslära inleds med en repetition av grundläggande matematikkunskaper om algebra, ekvationer, matriser, funktioner och derivata. Därefter behandlas linjär optimering, först i två variabler med fokus på geometrisk förståelse och därefter, i det allmänna fallet, med simplexmetoden. Denna metod tillämpas i boken även inom det spännande matematikområdet spelteori. Boken redogör för olika metoder för optimering av allmänna tvåvariabelfunktioner, dels över kompakta områden, dels med Lagranges sats givet ett bivillkor och dels med Hessianen. Boken tar avslutningsvis upp optimering på grafer med Kruskals, Prims och Dijkstras algoritmer.Boken vänder sig till studerande inom naturvetenskap, teknik eller ekonomi vid högskola och universitet. Boken kan också med fördel användas som en källa till fördjupning inom gymnasiets senare matematikkurser.

Det här är den andra boken i serien tipsboken. Den första boken utföll ett statistiksystem på 81 rader gällande topptipset med alla rätt den 5 januari i år och en utdelning på 73 809 kronor. Här i boken finns nya statistiksystem som du bara skriver av och lämnar in. Spelstrategi för matchen. System för oddset powerplay, tipset 1 x 2, V75, bomben, samt oddset.Resultat & utdelningar, samt statistik.Boken riktar sig till dig som vill vinna oftare och mer än vad du kanske gör idag.

A PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATEDThe revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems. The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared. The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers. The result has been a speed-up of several orders of magnitude. The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders’ decomposition. The revised second edition: Contains new developments on column generationOffers a new chapter on Benders’ algorithmIncludes expanded information on preprocessing, heuristics, and branch-and-cutPresents several basic and extended formulations, for example for fixed costnetwork flowsAlso touches on and briefly introduces topics such as non-bipartite matching, the complexity of extended formulations or a good linear program for the implementation of lift-and-project Written for students of integer/mathematical programming in operations research, mathematics, engineering, or computer science, Integer Programming offers an updated edition of the basic text that reflects the most recent developments in the field.

Mathematica by Example, Sixth Edition is an essential resource for the Mathematica user, providing step-by-step instructions on achieving results from this powerful software tool. The book fully accounts for the changes to functionality and visualization capabilities and accomodates the full array of new extensions in the types of data and problems that Mathematica can immediately handle, including cloud services and systems, geographic and geometric computation, dynamic visualization, interactive applications and other improvements. It is an ideal text for scientific students, researchers, and aspiring programmers seeking further understanding of Mathematica.

Written by seasoned practitioners with a view to practical implementation and problem-solving, the book's pedagogy is delivered clearly and without jargon using representative biological, physical and engineering problems. Code is provided on an ancillary website to support the use of Mathematica across diverse applications and subject areas.

Provides clear organization, integrated topic coverage, and accessible explanations Includes step-by-step instructions for the most popular implementations Contains new applications, exercises and examples from a variety of fields, including biology, physics and engineering Supported by online Mathematica code derived from examples in the book

This practical guide to optimization combines mathematical theory with hands-on coding examples to explore how Python can be used to model problems and obtain the best possible solutions. Presenting a balance of theory and practical applications, it is the ideal resource for upper-undergraduate and graduate students in applied mathematics, data science, business, industrial engineering and operations research, as well as practitioners in related fields. Beginning with an introduction to the concept of optimization, this text presents the key ingredients of an optimization problem and the choices one needs to make when modeling a real-life problem mathematically. Topics covered range from linear and network optimization to convex optimization and optimizations under uncertainty. The book's Python code snippets, alongside more than 50 Jupyter notebooks on the author's GitHub, allow students to put the theory into practice and solve problems inspired by real-life challenges, while numerous exercises sharpen students' understanding of the methods discussed.

Game theory means rigorous strategic thinking. It’s the art of anticipating your opponent’s next moves, knowing full well that your rival is trying to do the same thing to you. Though parts of game theory involve simple common sense, much is counterintuitive, and it can only be mastered by developing a new way of seeing the world. Using a diverse array of rich case studies—from pop culture, TV, movies, sports, politics, and history—the authors show how nearly every business and personal interaction has a game-theory component to it. Mastering game theory will make you more successful in business and life, and this lively book is the key to that mastery.

In recent years game theory has had a substantial impact on computer science, especially on Internet- and e-commerce-related issues. Algorithmic Game Theory, first published in 2007, develops the central ideas and results of this exciting area in a clear and succinct manner. More than 40 of the top researchers in this field have written chapters that go from the foundations to the state of the art. Basic chapters on algorithmic methods for equilibria, mechanism design and combinatorial auctions are followed by chapters on important game theory applications such as incentives and pricing, cost sharing, information markets and cryptography and security. This definitive work will set the tone of research for the next few years and beyond. Students, researchers, and practitioners alike need to learn more about these fascinating theoretical developments and their widespread practical application.

'Lucid, entertaining and precise... a brilliant warning about the gamification of everyday life' Tim Clare, GuardianIs this the game you want to be playing?Scoring systems are everywhere. Underpinning our daily lives – whether it’s the fit bits on our wrists, likes on social media, and even school rankings – they have become pervasive and increasingly dangerous, warping our desires and outsourcing our values to external institutions. Instead of encouraging us to be more playful, to take pleasure in the journey of striving towards a goal, institutions, corporations and bureaucracies weaponize scoring systems to impose their own interests. No matter what, we always seem to be playing by someone else’s rules.In The Score, philosopher C. Thi Nguyen shows us how this newly ‘gamified’ world has fundamentally captured our value systems, turning what might be moral or personal life choices into numerical data, and forcing us to prioritise what can be measured and monetized over what is truly meaningful to us.A life-long lover of online and board games himself, Nguyen argues that we should not stop playing games but rather take a step back and become more aware of their immersive and profound power, so that we might chart a way towards more creative and joyful lives. To start playing our own game.

Data-driven discovery is revolutionizing how we model, predict, and control complex systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and engineers for the next generation of scientific discovery by offering a broad overview of the growing intersection of data-driven methods, machine learning, applied optimization, and classical fields of engineering mathematics and mathematical physics. With a focus on integrating dynamical systems modeling and control with modern methods in applied machine learning, this text includes methods that were chosen for their relevance, simplicity, and generality. Topics range from introductory to research-level material, making it accessible to advanced undergraduate and beginning graduate students from the engineering and physical sciences. The second edition features new chapters on reinforcement learning and physics-informed machine learning, significant new sections throughout, and chapter exercises. Online supplementary material - including lecture videos per section, homeworks, data, and code in MATLAB®, Python, Julia, and R - available on databookuw.com.

The million copy international bestseller, critically acclaimed and translated into over 25 languages. As influential today as when it was first published, The Selfish Gene has become a classic exposition of evolutionary thought. Professor Dawkins articulates a gene's eye view of evolution - a view giving centre stage to these persistent units of information, and in which organisms can be seen as vehicles for their replication. This imaginative, powerful, and stylistically brilliant work not only brought the insights of Neo-Darwinism to a wide audience, but galvanized the biology community, generating much debate and stimulating whole new areas of research. Forty years later, its insights remain as relevant today as on the day it was published. This 40th anniversary edition includes a new epilogue from the author discussing the continuing relevance of these ideas in evolutionary biology today, as well as the original prefaces and foreword, and extracts from early reviews. Oxford Landmark Science books are 'must-read' classics of modern science writing which have crystallized big ideas, and shaped the way we think.

We all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory, and that the same principles of games like tag, dodgeball, and hide-and-seek are also at play in military strategy, high-seas chases by the Coast Guard, and even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics, from its classical analytical beginnings to the present day. Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an array of challenging puzzles with their historical background and broader applications. Chases and Escapes includes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis. Now with a gripping new preface on how the Enola Gay escaped the shock wave from the atomic bomb dropped on Hiroshima, this book will appeal to anyone interested in the mathematics that underlie pursuit and evasion.

This entertaining text is essential for anyone interested in game theory. Only a basic understanding of arithmetic is needed to grasp the necessary aspects of strategy games for two, three, four, and more players that feature two or more sets of inimical interests and a limitless array of zero-sum payoffs.

'BRILLIANTLY CLEAR AND CAPTIVATING PROSE' STEPHEN FRY A WATERSTONES BOOK OF YEAR 2023 An award-winning mathematician explores the maths behind the games we love and why we love to play them. Where should you move first in Connect 4? Which property is best in Monopoly? How can pi help you win Rock Paper Scissors? Crossing oceans, continents and millennia, award-winning mathematician Marcus du Sautoy explores how maths and games have always been deeply intertwined. As well as being integral to human psychology and culture throughout the ages, games provided the first opportunities for deep mathematical insight into the world. This grand adventure teaches us how to strategise, play better and win more often.‘The subject matter is fun (I mean, isn’t it quite literally the definition of fun?) and du Sautoy’s enthusiasm is infectious’ THE SUNDAY TIMES‘Lively, creative and humane – exactly as one would expect from Marcus du Sautoy’ TIM HARFORD, author of How To Make The World Add Up'A delightful and addictive celebration of games. You’ll keep wanting one more go' DARA Ó BRIAIN, author of Is There Anybody Out There?‘You do not need to be a seasoned player nor a skilled mathematician to relish this enchanting read. However, this book may just encourage you to become one or the other’ REINER KNIZIA, award-winning game designer

'BRILLIANTLY CLEAR AND CAPTIVATING PROSE' STEPHEN FRY A WATERSTONES BOOK OF YEAR 2023 An award-winning mathematician explores the maths behind the games we love and why we love to play them. Where should you move first in Connect 4?What is the best property in Monopoly?And how can pi help you win rock paper scissors?Spanning millennia, oceans and continents, countries and cultures, Around the World in 80 Games gleefully explores how mathematics and games have always been deeply intertwined. Marcus du Sautoy investigates how games provided the first opportunities for deep mathematical insight into the world, how understanding maths can help us play games better, and how both maths and games are integral to human psychology and culture.For as long as there have been people, there have been games, and for nearly as long, we have been exploring and discovering mathematics. A grand adventure, Around the World in 80 Games teaches us not just how games are won, but how they, and the maths behind them, shape who we are. 'A delightful and addictive celebration of games. You’ll keeping wanting one more go' DARA Ó BRIAIN ‘Whether your game is Go, Dungeons and Dragons, or Chocolate Chilli Roulette, you'll find this book adorable. It's lively, creative and humane – exactly as one would expect from Marcus du Sautoy’ TIM HARFORD, author of How To Make The World Add Up

'BRILLIANTLY CLEAR AND CAPTIVATING PROSE' STEPHEN FRY A WATERSTONES BOOK OF YEAR 2023 An award-winning mathematician explores the maths behind the games we love and why we love to play them. Where should you move first in Connect 4?Which property is best in Monopoly?How can pi help you win Rock Paper Scissors?Crossing oceans, continents and millennia, award-winning mathematician Marcus du Sautoy explores how maths and games have always been deeply intertwined. As well as being integral to human psychology and culture throughout the ages, games provided the first opportunities for deep mathematical insight into the world. This grand adventure teaches us how to strategise, play better and win more often.‘The subject matter is fun (I mean, isn’t it quite literally the definition of fun?) and du Sautoy’s enthusiasm is infectious’ THE SUNDAY TIMES'A delightful and addictive celebration of games. You’ll keep wanting one more go' DARA Ó BRIAIN, author of Is There Anybody Out There?‘Lively, creative and humane – exactly as one would expect from Marcus du Sautoy’ TIM HARFORD, author of How To Make The World Add Up‘You do not need to be a seasoned player nor a skilled mathematician to relish this enchanting read. However, this book may just encourage you to become the one or the other’ REINER KNIZIA, award-winning game designer

"Game Theory for Economists" introduces economists to the game-theoretic approach of modelling economic behaviour and interaction, focusing on concepts and ideas from the vast field of game-theoretic models which find commonly used applications in economics. This careful selection of topics allows the reader to concentrate on the parts of the game which are the most relevant for the economist who does not want to become a specialist. Written at a level appropriate for a student or researcher with a solid microeconomic background, the book should provide the reader with skills necessary to formalize economic games and to make them accessible for game theoretic analysis. It offers a concise introduction to game theory which provides economists with the techniques and results necessary to follow the literature in economic theory; helps the reader formalize economic problems; and, concentrates on equilibrium concepts that are most commonly used in economics.

This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as case studies around portfolio insurance and risk estimation problems. In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website.

Shows ways to build and implement tools that help test ideas Focuses on the application of heuristics; standard methods receive limited attention Presents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models

Mathematical optimization is used in nearly all computer graphics applications, from computer vision to animation. This book teaches readers the core set of techniques that every computer graphics professional should understand in order to envision and expand the boundaries of what is possible in their work.

Study of this authoritative reference will help readers develop a very powerful tool- the ability to create and decipher mathematical models that can better realize solutions to even the toughest problems confronting computer graphics community today.

Distills down a vast and complex world of information on optimization into one short, self-contained volume especially for computer graphics Helps CG professionals identify the best technique for solving particular problems quickly, by categorizing the most effective algorithms by application Keeps readers current by supplementing the focus on key, classic methods with special end-of-chapter sections on cutting-edge developments

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.

Highlighted definitions, rules, methods, and procedures, and abundant tables, diagrams, and graphs, clearly illustrate important concepts and methods Provides end-of-chapter vocabulary and concept reviews, as well as robust review exercises and a practice test Contains information relevant to a wide range of topics, including symbolic language, contemporary math, liberal arts math, social sciences math, basic math for finance, math for humanities, probability, and the C.L.A.S.T. exam Optional advanced sections and challenging problems are included for use at the discretion of the instructor Online resources include PowerPoint Presentations for instructors and a useful student manual

The Gradient Test: Another Likelihood-Based Test presents the latest on the gradient test, a large-sample test that was introduced in statistics literature by George R. Terrell in 2002. The test has been studied by several authors, is simply computed, and can be an interesting alternative to the classical large-sample tests, namely, the likelihood ratio (LR), Wald (W), and Rao score (S) tests.

Due to the large literature about the LR, W and S tests, the gradient test is not frequently used to test hypothesis. The book covers topics on the local power of the gradient test, the Bartlett-corrected gradient statistic, the gradient statistic under model misspecification, and the robust gradient-type bounded-influence test.

Covers the background of the gradient statistic and the different models Discusses The Bartlett-corrected gradient statistic Explains the algorithm to compute the gradient-type statistic

Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development.

This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena.

The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians.

Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear.

Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations & inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spaces.

Systematic analysis of existence theory and topological structure of solution sets for fractional evolution inclusions and control systems Differential models with fractional derivative provide an excellent instrument for the description of memory and hereditary properties, and their description and working will provide valuable insights into the modelling of many physical phenomena suitable for engineers and physicists The book provides the necessary background material required to go further into the subject and explore the rich research literature

Mathematical Optimization Terminology: A Comprehensive Glossary of Terms is a practical book with the essential formulations, illustrative examples, real-world applications and main references on the topic.

This book helps readers gain a more practical understanding of optimization, enabling them to apply it to their algorithms. This book also addresses the need for a practical publication that introduces these concepts and techniques.

Discusses real-world applications of optimization and how it can be used in algorithms Explains the essential formulations of optimization in mathematics Covers a more practical approach to optimization

Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical background and practical implementation, complements extensive literature with well-chosen case studies to illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms, simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search, algorithm analysis, constraint handling, hybrid methods, parameter tuning and control, as well as multi-objective optimization.

This book can serve as an introductory book for graduates, doctoral students and lecturers in computer science, engineering and natural sciences. It can also serve a source of inspiration for new applications. Researchers and engineers as well as experienced experts will also find it a handy reference.

Discusses and summarizes the latest developments in nature-inspired algorithms with comprehensive, timely literature Provides a theoretical understanding as well as practical implementation hints Provides a step-by-step introduction to each algorithm