Linear Optimization and Dualiyy: A Modern Exposition departs from convention in significant ways. Standard linear programming textbooks present the material in the order in which it was discovered. Duality is treated as a difficult add-on after coverage of formulation, the simplex method, and polyhedral theory. Students end up without knowing duality in their bones. This text brings in duality in Chapter 1 and carries duality all the way through the exposition. Chapter 1 gives a general definition of duality that shows the dual aspects of a matrix as a column of rows and a row of columns. The proof of weak duality in Chapter 2 is shown via the Lagrangian, which relies on matrix duality. The first three LP formulation examples in Chapter 3 are classic primal-dual pairs including the diet problem and 2-person zero sum games. For many engineering students, optimization is their first immersion in rigorous mathematics. Conventional texts assume a level of mathematical sophistication they don't have. This text embeds dozens of reading tips and hundreds of answered questions to guide such students. Features Emphasis on duality throughout Practical tips for modeling and computation Coverage of computational complexity and data structures Exercises and problems based on the learning theory concept of the zone of proximal development Guidance for the mathematically unsophisticated reader About the Author Craig A. Tovey is a professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. Dr. Tovey received an AB from Harvard College, an MS in computer science and a PhD in operations research from Stanford University. His principal activities are in operations research and its interdisciplinary applications. He received a Presidential Young Investigator Award and the Jacob Wolfowitz Prize for research in heuristics. He was named an Institute Fellow at Georgia Tech, and was recognized by the ACM Special Interest Group on Electronic Commerce with the Test of Time Award. Dr. Tovey received the 2016 Golden Goose Award for his research on bee foraging behavior leading to the development of the Honey Bee Algorithm.

This book presents simple, elegant methods for dealing, both in theory and in application, with a variety of problems that have formulations in terms of flows in capacity-constrained networks. Since the theoretical considerations lead in all cases to computationally efficient solution procedures, the hook provides a common meeting ground for persons interested in operations research, industrial and communications engineering, or combinatorial mathematics. Originally published in 1962. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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.

Filling the need for an introductory book on linear programming that discusses the important ways to mitigate parameter uncertainty, Introduction to Linear Optimization and Extensions with MATLAB(r) provides a concrete and intuitive yet rigorous introduction to modern linear optimization. In addition to fundamental topics, the book discusses current linear optimization technologies such as predictor-path following interior point methods for both linear and quadratic optimization as well as the inclusion of linear optimization of uncertainty i.e. stochastic programming with recourse and robust optimization.

The author introduces both stochastic programming and robust optimization as frameworks to deal with parameter uncertainty. The author s unusual approach developing these topics in an introductory book highlights their importance. Since most applications require decisions to be made in the face of uncertainty, the early introduction of these topics facilitates decision making in real world environments. The author also includes applications and case studies from finance and supply chain management that involve the use of MATLAB.

Even though there are several LP texts in the marketplace, most do not cover data uncertainty using stochastic programming and robust optimization techniques. Most emphasize the use of MS Excel, while this book uses MATLAB which is the primary tool of many engineers, including financial engineers. The book focuses on state-of-the-art methods for dealing with parameter uncertainty in linear programming, rigorously developing theory and methods. But more importantly, the author s meticulous attention to developing intuition before presenting theory makes the material come alive. "

The late George B. Dantzig, widely known as the father of linear programming, was a major influence in mathematics, operations research, and economics. As Professor Emeritus at Stanford University, he continued his decades of research on linear programming and related subjects. Dantzig was awarded eight honorary doctorates, the National Medal of Science, and the John von Neumann Theory Prize from the Institute for Operations Research and the Management Sciences.
The 24 chapters of this volume highlight the amazing breadth and enduring influence of Dantzig's research. Short, non-technical summaries at the opening of each major section introduce a specific research area and discuss the current significance of Dantzig's work in that field. Among the topics covered are mathematical statistics, the Simplex Method of linear programming, economic modeling, network optimization, and nonlinear programming. The book also includes a complete bibliography of Dantzig's writings.

This book provides an introduction to the use of nonlinear modelling in medical statistics, including worked through examples in most areas where such techniques are used. It is suitable for both professional and academic statisticians working in medical research. The data and computer code for the examples will be available on the authors web site.

Written in a conversational tone, this classroom-tested text introduces the fundamentals of linear programming and game theory, showing readers how to apply serious mathematics to practical real-life questions by modelling linear optimization problems and strategic games. The treatment of linear programming includes two distinct graphical methods. The game theory chapters include a novel proof of the minimax theorem for 2x2 zero-sum games. In addition to zero-sum games, the text presents variable-sum games, ordinal games, and n-player games as the natural result of relaxing or modifying the assumptions of zero-sum games. All concepts and techniques are derived from motivating examples, building in complexity, which encourages students to think creatively and leads them to understand how the mathematics is applied. With no prerequisite besides high school algebra, the text will be useful to motivated high school students and undergraduates studying business, economics, mathematics, and the social sciences.

Written in a conversational tone, this classroom-tested text introduces the fundamentals of linear programming and game theory, showing readers how to apply serious mathematics to practical real-life questions by modelling linear optimization problems and strategic games. The treatment of linear programming includes two distinct graphical methods. The game theory chapters include a novel proof of the minimax theorem for 2x2 zero-sum games. In addition to zero-sum games, the text presents variable-sum games, ordinal games, and n-player games as the natural result of relaxing or modifying the assumptions of zero-sum games. All concepts and techniques are derived from motivating examples, building in complexity, which encourages students to think creatively and leads them to understand how the mathematics is applied. With no prerequisite besides high school algebra, the text will be useful to motivated high school students and undergraduates studying business, economics, mathematics, and the social sciences.

The authoritative guide to modeling and solving complex problems with linear programming--extensively revised, expanded, and updated

The only book to treat both linear programming techniques and network flows under one cover, "Linear Programming and Network Flows, Fourth Edition" has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research, computer science, and mathematics.

The book begins with basic results on linear algebra and convex analysis, and a geometrically motivated study of the structure of polyhedral sets is provided. Subsequent chapters include coverage of cycling in the simplex method, interior point methods, and sensitivity and parametric analysis. Newly added topics in the "Fourth Edition" include:

The cycling phenomenon in linear programming and the geometry of cycling

Duality relationships with cycling

Elaboration on stable factorizations and implementation strategies

Stabilized column generation and acceleration of Benders and Dantzig-Wolfe decomposition methods

Line search and dual ascent ideas for the out-of-kilter algorithm

Heap implementation comments, negative cost circuit insights, and additional convergence analyses for shortest path problems

The authors present concepts and techniques that are illustrated by numerical examples along with insights complete with detailed mathematical analysis and justification. An emphasis is placed on providing geometric viewpoints and economic interpretations as well as strengthening the understanding of the fundamental ideas. Each chapter is accompanied by "Notes" and "References" sections that provide historical developments in addition to current and future trends. Updated exercises allow readers to test their comprehension of the presented material, and extensive references provide resources for further study.

"Linear Programming and Network Flows, Fourth Edition" is an excellent book for linear programming and network flow courses at the upper-undergraduate and graduate levels. It is also a valuable resource for applied scientists who would like to refresh their understanding of linear programming and network flow techniques.

A semantically well-defined programming language widely used in artificial intelligence, Prolog has greatly influenced other programming languages since its introduction in the late 1970s. A user may find Prolog deceptively easy, however, and there are a number of different implementations. In this book Patrice Boizumault draws from his extensive experience in Prolog implementation to describe for students of all levels the concepts, difficulties, and design limits of a Prolog system.

Boizumault introduces the specific problems posed by the implementation of Prolog, studies and compares different solutions--notably those of the schools of Marseilles and Edinburgh--and concludes with three examples of implementation. Major points of interest include identifying the important differences in implementing unification and resolution; presenting three features of Prolog II--infinite trees, "dif," and "freeze"--that introduce constraints; thoroughly describing Warren's Abstract Machine (WAM); and detailing a Lisp imple-mentation of Prolog.

Originally published in 1993.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This book constitutes the refereed proceedings of the 18th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2016, held in Liege, Belgium, in June 2016. The 33 full papers presented were carefully reviewed and selected from 125 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.

This book constitutes the refereed proceedings of the 10th International Workshop on Hybrid Metaheuristics, HM 2016, held in Plymouth, UK, in June 2016. The 15 revised full papers presented were carefully reviewed and selected from 43 submissions. The selected papers are of interest for all the researchers working on integrating metaheuristics with other areas for solving both optimization and constraint satisfaction problems. They represent as well a sample of current research demonstrating how metaheuristics can be integrated with integer linear programming and other operational research techniques for tackling difficult and relevant problems.

An essential introduction to the analysis and verification of control system software The verification of control system software is critical to a host of technologies and industries, from aeronautics and medical technology to the cars we drive. The failure of controller software can cost people their lives. In this authoritative and accessible book, Pierre-Loic Garoche provides control engineers and computer scientists with an indispensable introduction to the formal techniques for analyzing and verifying this important class of software. Too often, control engineers are unaware of the issues surrounding the verification of software, while computer scientists tend to be unfamiliar with the specificities of controller software. Garoche provides a unified approach that is geared to graduate students in both fields, covering formal verification methods as well as the design and verification of controllers. He presents a wealth of new verification techniques for performing exhaustive analysis of controller software. These include new means to compute nonlinear invariants, the use of convex optimization tools, and methods for dealing with numerical imprecisions such as floating point computations occurring in the analyzed software. As the autonomy of critical systems continues to increase-as evidenced by autonomous cars, drones, and satellites and landers-the numerical functions in these systems are growing ever more advanced. The techniques presented here are essential to support the formal analysis of the controller software being used in these new and emerging technologies.

Das Buch gibt eine Einfuhrung in das neue Gebiet der Analyse und Optimierung von Tragwerken unter stochastischer Unsicherheit. Es werden die Grundlagen ausfuhrlich dargestellt und zum Teil von unterschiedlichen Standpunkten aus beleuchtet.

In Teil I wird die lineare Theorie der Stabtragwerke als Grundlage fur die FEM entwickelt. Vorausgesetzt werden dabei nur wenige Kenntnisse aus der Technischen Mechanik und der Ingenieurmathematik, insbesondere eine gewisse Vertrautheit mit der Matrizenrechnung.

In Teil II wird dargestellt, wie sich die Wahrscheinlichkeitsverteilungen der Verschiebungen und Spannungen in den Knoten aus denen der stochastischen Stabparameter und ausseren Lasten - zumindest approximativ - berechnen lassen.

In Teil III schliesslich wird die Optimierung von Tragwerken mit stochastischen Parametern behandelt. Dazu wird ein geeignetes deterministisches Ersatzproblem des Ausgangsproblems mit stochastischen Modellparametern formuliert.

Eine kurze Beschreibung einiger Optimierungsverfahren findet man im letzten Abschnitt. Besondere Muhe wurde auf die zahlreichen und eingehend behandelten Beispiele verwandt.

Das Buch ist geschrieben fur Studierende, praktisch tatige Ingenieure und Mathematiker. "

Mechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design.

Metaheuristics support managers in decision-making with robust tools that provide high-quality solutions to important applications in business, engineering, economics, and science in reasonable time frames, but finding exact solutions in these applications still poses a real challenge. However, because of advances in the fields of mathematical optimization and metaheuristics, major efforts have been made on their interface regarding efficient hybridization.

This edited book will provide a survey of the state of the art in this field by providing some invited reviews by well-known specialists as well as refereed papers from the second Matheuristics workshop to be held in Bertinoro, Italy, June 2008. Papers will explore mathematical programming techniques in metaheuristics frameworks, and especially focus on the latest developments in Mixed Integer Programming in solving real-world problems.

It is well known that a large number of problems relevant to the control ?eld can be formulatedas optimizationproblems. For long time, the classical approachhas been to look for a closed form solution to the speci?c optimizationproblems at hand. The last decade has seen a noticeable shift in the meaning of "closed form" solution. The formidable increase of computationalpower has dramatically changed the fe- ing of theoreticians as well as of practitioners about what is meant by tractable and untractableproblems. A main issue regardsconvexity. From a theoretical viewpoint, there has been a large amount of work in the directions of "convexifying" nonc- vex problems and studying structural features of convex problems. On the other hand, extremely powerful algorithmsfor the solution of convexproblemshave been devised in the last two decades. Clearly, the fact that a wide variety of engine- ing problems can be formulated as convex problems has strongly motivated efforts in this direction. The control ?eld is not an exception in this sense: many pr- lems in robust control, identi?cation and nonlinear control have been recognized as convex problems. Moreover, convex relaxations of nonconvex problems have been intensively investigated, as they provide an effective tool for bounding the optimal solution of the original problem. As far as robust control is concerned, it is known since long time that several classes of problemscan be reducedto testing positivity of suitable polynomials.

The significant progress that has been made in recent years both in hardware implementations and in numerical computing has rendered real-time optimization-based control a viable option when it comes to advanced industrial applications. More recently, the need for control of a process in the presence of a limited amount of hardware resources has triggered research in the direction of embedded optimization-based control. Operator Splitting Methods in Control focuses on systems with linear dynamics, giving rise to convex control problems. It provides a comprehensive survey of a family of first order methods known as decomposition schemes or operator splitting methods and shows the behavior of such algorithms as solvers of control related convex problems from tens to a few hundreds of variables. This compact survey gives the reader a state-of-the-art overview of the topic with examples of applications in aerospace and building control.

The unique feature of this compact student's introduction to Mathematica (R) and the Wolfram Language (TM) is that the order of the material closely follows a standard mathematics curriculum. As a result, it provides a brief introduction to those aspects of the Mathematica (R) software program most useful to students. Used as a supplementary text, it will help bridge the gap between Mathematica (R) and the mathematics in the course, and will serve as an excellent tutorial for former students. There have been significant changes to Mathematica (R) since the second edition, and all chapters have now been updated to account for new features in the software, including natural language queries and the vast stores of real-world data that are now integrated through the cloud. This third edition also includes many new exercises and a chapter on 3D printing that showcases the new computational geometry capabilities that will equip readers to print in 3D.