"The purpose of the book is to give the reader a working knowledge of optimization theory and methods"--
An up-to-date, accessible introduction to an increasingly important field This timely and authoritative book fills a growing need for an introductory text to optimization methods and theory at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked-out examples to illustrate both theory and algorithms, this book also provides: A review of the required mathematical background material A mathematical discussion at a level accessible to MBA and business students A treatment of both linear and nonlinear programming An introduction to the most recent developments, including neural networks, genetic algorithms, and the nonsimplex method of Karmarkar A chapter on the use of descent algorithms for the training of feedforward neural networks Exercise problems after every chapter MATLAB exercises and examples An optional solutions manual with MATLAB source listings This book helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business.
Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.
New, significant scientific discoveries in laser and photonic technologies, systems perspectives, and integrated design approaches can improve even further the impact in critical areas of challenge. Yet this knowledge is dispersed across several disciplines and research arenas. Laser and Photonic Systems: Design and Integration brings together a multidisciplinary group of experts to increase understanding of the ways in which systems perspectives may influence laser and photonic innovations and application integration. By bringing together chapters from leading scientists and technologists, industrial and systems engineers, and managers, the book stimulates new thinking that would bring a systems, network, and system-of-systems perspective to bear on laser and photonic systems applications. The chapters challenge you to explore opportunities for revolutionary and broader advancements. The authors emphasize the identification of emerging research and application frontiers where there are promising contributions to lasers, optics, and photonics applications in fields such as manufacturing, healthcare, security, and communications. The book contains insights from leading researchers, inventors, implementers, and innovators. It explains a variety of techniques, models, and technologies proven to work with laser and photonic systems, their development, design, and integration. Such systems are of growing interest to many organizations, given their promise and potential solutions of grand societal challenges. Lastly, the book helps you leverage the knowledge into exciting new frontiers of successful solutions.
Wiley-Interscience Series in Discrete Mathematics and Optimization Advisory Editors Ronald L. Graham Jan Karel Lenstra Robert E. Tarjan Discrete Mathematics and Optimization involves the study of finite structures. It is one of the fastest growing areas in mathematics today. The level and depth of recent advances in the area and the wide applicability of its evolving techniques point to the rapidity with which the field is moving from its beginnings to maturity and presage the ever-increasing interaction between it and computer science. The Series provides a broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, mathematical programming and the analysis of algorithms, and including such topics as Ramsey theory, transversal theory, block designs, finite geometries, Polya theory, graph and matroid algorithms, network flows, polyhedral combinatorics and computational complexity. The Wiley - Interscience Series in Discrete Mathematics and Optimization will be a substantial part of the record of this extraordinary development. Recent titles in the Series: Search Problems Rudolf Ahlswede, University of Bielefeld, Federal Republic of Germany Ingo Wegener, Johann Wolfgang Goethe University, Frankfurt, Federal Republic of Germany The problems of search, exploration, discovery and identification are of key importance in a wide variety of applications. This book will be of great interest to all those concerned with searching, sorting, information processing, design of experiments and optimal allocation of resources. 1987 Introduction to Optimization E. M. L. Beale FRS, Scicon Ltd, Milton Keynes, and Imperial College, London This book is intended as an introduction to the many topics covered by the term 'optimization', with special emphasis on applications in industry. It is divided into three parts. The first part covers unconstrained optimization, the second describes the methods used to solve linear programming problems, and the third covers nonlinear programming, integer programming and dynamic programming. The book is intended for senior undergraduate and graduate students studying optimization as part of a course in mathematics, computer science or engineering. 1988
A timely, accessible introduction to the mathematics ofchaos. The past three decades have seen dramatic developments in thetheory of dynamical systems, particularly regarding the explorationof chaotic behavior. Complex patterns of even simple processesarising in biology, chemistry, physics, engineering, economics, anda host of other disciplines have been investigated, explained, andutilized. Introduction to Discrete Dynamical Systems and Chaos makes theseexciting and important ideas accessible to students and scientistsby assuming, as a background, only the standard undergraduatetraining in calculus and linear algebra. Chaos is introduced at theoutset and is then incorporated as an integral part of the theoryof discrete dynamical systems in one or more dimensions. Both phasespace and parameter space analysis are developed with ampleexercises, more than 100 figures, and important practical examplessuch as the dynamics of atmospheric changes and neuralnetworks. An appendix provides readers with clear guidelines on how to useMathematica to explore discrete dynamical systems numerically.Selected programs can also be downloaded from a Wiley ftp site(address in preface). Another appendix lists possible projects thatcan be assigned for classroom investigation. Based on the author's1993 book, but boasting at least 60% new, revised, and updatedmaterial, the present Introduction to Discrete Dynamical Systemsand Chaos is a unique and extremely useful resource for allscientists interested in this active and intensely studiedfield. An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.
A unique interdisciplinary foundation for real-world problemsolving Stochastic search and optimization techniques are used in a vastnumber of areas, including aerospace, medicine, transportation, andfinance, to name but a few. Whether the goal is refining the designof a missile or aircraft, determining the effectiveness of a newdrug, developing the most efficient timing strategies for trafficsignals, or making investment decisions in order to increaseprofits, stochastic algorithms can help researchers andpractitioners devise optimal solutions to countless real-worldproblems. Introduction to Stochastic Search and Optimization: Estimation,Simulation, and Control is a graduate-level introduction to theprinciples, algorithms, and practical aspects of stochasticoptimization, including applications drawn from engineering,statistics, and computer science. The treatment is both rigorousand broadly accessible, distinguishing this text from much of thecurrent literature and providing students, researchers, andpractitioners with a strong foundation for the often-daunting taskof solving real-world problems. The text covers a broad range of today’s most widely usedstochastic algorithms, including: Random search Recursive linear estimation Stochastic approximation Simulated annealing Genetic and evolutionary methods Machine (reinforcement) learning Model selection Simulation-based optimization Markov chain Monte Carlo Optimal experimental design The book includes over 130 examples, Web links to software anddata sets, more than 250 exercises for the reader, and an extensivelist of references. These features help make the text an invaluableresource for those interested in the theory or practice ofstochastic search and optimization.
Algorithmic discrete mathematics plays a key role in the development of information and communication technologies, and methods that arise in computer science, mathematics and operations research – in particular in algorithms, computational complexity, distributed computing and optimization – are vital to modern services such as mobile telephony, online banking and VoIP. This book examines communication networking from a mathematical viewpoint. The contributing authors took part in the European COST action 293 – a four-year program of multidisciplinary research on this subject. In this book they offer introductory overviews and state-of-the-art assessments of current and future research in the fields of broadband, optical, wireless and ad hoc networks. Particular topics of interest are design, optimization, robustness and energy consumption. The book will be of interest to graduate students, researchers and practitioners in the areas of networking, theoretical computer science, operations research, distributed computing and mathematics.
A complete, highly accessible introduction to one of today's mostexciting areas of applied mathematics One of the youngest, most vital areas of applied mathematics,combinatorial optimization integrates techniques fromcombinatorics, linear programming, and the theory of algorithms.Because of its success in solving difficult problems in areas fromtelecommunications to VLSI, from product distribution to airlinecrew scheduling, the field has seen a ground swell of activity overthe past decade. Combinatorial Optimization is an ideal introduction to thismathematical discipline for advanced undergraduates and graduatestudents of discrete mathematics, computer science, and operationsresearch. Written by a team of recognized experts, the text offersa thorough, highly accessible treatment of both classical conceptsand recent results. The topics include: * Network flow problems * Optimal matching * Integrality of polyhedra * Matroids * NP-completeness Featuring logical and consistent exposition, clear explanations ofbasic and advanced concepts, many real-world examples, and helpful,skill-building exercises, Combinatorial Optimization is certain tobecome the standard text in the field for many years to come.
An intuitive and accessible approach to discrete mathematics using Latin squares In the past two decades, researchers have discovered a range of uses for Latin squares that go beyond standard mathematics. People working in the fields of science, engineering, statistics, and even computer science all stand to benefit from a working knowledge of Latin squares. Discrete Mathematics Using Latin Squares is the only upper-level college textbook/professional reference that fully engages the subject and its many important applications. Mixing theoretical basics, such as the construction of orthogonal Latin squares, with numerous practical examples, proofs, and exercises, this text/reference offers an extensive and well-rounded treatment of the topic. Its flexible design encourages readers to group chapters according to their interests, whether they be purely mathematical or mostly applied. Other features include: An entirely new approach to discrete mathematics, from basic properties and generalizations to unusual applications 16 self-contained chapters that can be grouped for custom use Coverage of various uses of Latin squares, from computer systems to tennis and golf tournament design An extensive range of exercises, from routine problems to proofs of theorems Extended coverage of basic algebra in an appendix filled with corresponding material for further investigation. Written by two leading authorities who have published extensively in the field, Discrete Mathematics Using Latin Squares is an easy-to-use academic and professional reference.
Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index
Introduction to Dynamic Programming provides information pertinent to the fundamental aspects of dynamic programming. This book considers problems that can be quantitatively formulated and deals with mathematical models of situations or phenomena that exists in the real world. Organized into 10 chapters, this book begins with an overview of the fundamental components of any mathematical optimization model. This text then presents the details of the application of dynamic programming to variational problems. Other chapters consider the application of dynamic programming to inventory theory, Markov processes, chemical engineering, optimal control theory, calculus of variations, and economics. This book discusses as well the approach to problem solving that is typical of dynamic programming. The final chapter deals with a number of actual applications of dynamic programming to practical problems. This book is a valuable resource for .graduate level students of mathematics, economics, statistics, business, operations research, industrial engineering, or other engineering fields.
Merging logic and mathematics in deductive inference-an innovative,cutting-edge approach. Optimization methods for logical inference? Absolutely, say VijayChandru and John Hooker, two major contributors to this rapidlyexpanding field. And even though "solving logical inferenceproblems with optimization methods may seem a bit like eatingsauerkraut with chopsticks. . . it is the mathematical structure ofa problem that determines whether an optimization model can helpsolve it, not the context in which the problem occurs." Presenting powerful, proven optimization techniques for logicinference problems, Chandru and Hooker show how optimization modelscan be used not only to solve problems in artificial intelligenceand mathematical programming, but also have tremendous applicationin complex systems in general. They survey most of the recentresearch from the past decade in logic/optimization interfaces,incorporate some of their own results, and emphasize the types oflogic most receptive to optimization methods-propositional logic,first order predicate logic, probabilistic and related logics,logics that combine evidence such as Dempster-Shafer theory, rulesystems with confidence factors, and constraint logic programmingsystems. Requiring no background in logic and clearly explaining all topicsfrom the ground up, Optimization Methods for Logical Inference isan invaluable guide for scientists and students in diverse fields,including operations research, computer science, artificialintelligence, decision support systems, and engineering.
A lively invitation to the flavor, elegance, and power of graphtheory This mathematically rigorous introduction is tempered and enlivenedby numerous illustrations, revealing examples, seductiveapplications, and historical references. An award-winning teacher,Russ Merris has crafted a book designed to attract and engagethrough its spirited exposition, a rich assortment of well-chosenexercises, and a selection of topics that emphasizes the kinds ofthings that can be manipulated, counted, and pictured. Intendedneither to be a comprehensive overview nor an encyclopedicreference, this focused treatment goes deeply enough into asufficiently wide variety of topics to illustrate the flavor,elegance, and power of graph theory. Another unique feature of the book is its user-friendly modularformat. Following a basic foundation in Chapters 1-3, the remainderof the book is organized into four strands that can be exploredindependently of each other. These strands center, respectively,around matching theory; planar graphs and hamiltonian cycles;topics involving chordal graphs and oriented graphs that naturallyemerge from recent developments in the theory of graphic sequences;and an edge coloring strand that embraces both Ramsey theory and aself-contained introduction to Pólya's enumeration ofnonisomorphic graphs. In the edge coloring strand, the reader ispresumed to be familiar with the disjoint cycle factorization of apermutation. Otherwise, all prerequisites for the book can be foundin a standard sophomore course in linear algebra. The independence of strands also makes Graph Theory an excellentresource for mathematicians who require access to specific topicswithout wanting to read an entire book on the subject.
Das Lehrbuch ist die deutsche Übersetzung der 4., wesentlich erweiterten Auflage des Titels „Combinatorial Optimization – Theory and Algorithms". Es gibt den neuesten Stand der kombinatorischen Optimierung wieder und liefert vornehmlich theoretische Resultate und Algorithmen mit beweisbar guten Laufzeiten und Ergebnissen, jedoch keine Heuristiken. Enthalten sind vollständige Beweise, auch für viele tiefe und neue Resultate, von denen einige bisher in der Lehrbuchliteratur noch nicht erschienen sind. Mit Übungen und umfassendem Literaturverzeichnis.
Very Good,No Highlights or Markup,all pages are intact.
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.
Decision Theory An Introduction to Dynamic Programming and Sequential Decisions John Bather University of Sussex, UK Mathematical induction, and its use in solving optimization problems, is a topic of great interest with many applications. It enables us to study multistage decision problems by proceeding backwards in time, using a method called dynamic programming. All the techniques needed to solve the various problems are explained, and the author's fluent style will leave the reader with an avid interest in the subject. * Tailored to the needs of students of optimization and decision theory * Written in a lucid style with numerous examples and applications * Coverage of deterministic models: maximizing utilities, directed networks, shortest paths, critical path analysis, scheduling and convexity * Coverage of stochastic models: stochastic dynamic programming, optimal stopping problems and other special topics * Coverage of advanced topics: Markov decision processes, minimizing expected costs, policy improvements and problems with unknown statistical parameters * Contains exercises at the end of each chapter, with hints in an appendix Aimed primarily at students of mathematics and statistics, the lucid text will also appeal to engineering and science students and those working in the areas of optimization and operations research.
The first comprehensive review of the theory and practice of one oftoday's most powerful optimization techniques. The explosive growth of research into and development of interiorpoint algorithms over the past two decades has significantlyimproved the complexity of linear programming and yielded some oftoday's most sophisticated computing techniques. This book offers acomprehensive and thorough treatment of the theory, analysis, andimplementation of this powerful computational tool. Interior Point Algorithms provides detailed coverage of all basicand advanced aspects of the subject. Beginning with an overview offundamental mathematical procedures, Professor Yinyu Ye movesswiftly on to in-depth explorations of numerous computationalproblems and the algorithms that have been developed to solve them.An indispensable text/reference for students and researchers inapplied mathematics, computer science, operations research,management science, and engineering, Interior Point Algorithms: * Derives various complexity results for linear and convexprogramming * Emphasizes interior point geometry and potential theory * Covers state-of-the-art results for extension, implementation,and other cutting-edge computational techniques * Explores the hottest new research topics, including nonlinearprogramming and nonconvex optimization.