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Item specifics

Condition
New: A new, unread, unused book in perfect condition with no missing or damaged pages. See the ...
Book Title
Linear Optimization and Duality: A Modern Exposition
Publication Date
2020-12-16
Pages
586
ISBN
9781439887462

About this product

Product Identifiers

Publisher
CRC Press LLC
ISBN-10
1439887462
ISBN-13
9781439887462
eBay Product ID (ePID)
109294310

Product Key Features

Number of Pages
480 Pages
Publication Name
Linear Programming with Duals : a Modern Exposition
Language
English
Publication Year
2019
Subject
Operations Research, Linear & Nonlinear Programming, Applied
Type
Textbook
Subject Area
Mathematics, Technology & Engineering, Business & Economics
Author
Craig A. Tovey
Format
Hardcover

Dimensions

Item Length
9.2 in
Item Width
6.1 in

Additional Product Features

Intended Audience
College Audience
Dewey Edition
23
Illustrated
Yes
Dewey Decimal
519.72
Table Of Content
Introduction Notation What Is Linear Programming? Visualizing LP Presolving LP Problems Formulating and Solving Linear Programs Three Classic Primal/Dual Formulation Pairs LP Modeling Methods More Examples of LP Formulation Using Software to Solve LPs Dual Variables as Shadow Prices Problems Polyhedra Separation Fourier-Motzkin Elimination Theorems of the Alternative Extreme Points and Optimal Solutions Two Ways to Represent Polyhedra Problems The Simplex Method and Its Variants The Simplex Method Complications Variants High Level Computational Issues The Geography of Mount Duality Variants of Farkas's Lemma and of Strong Duality To and From Helly's Theorem Other Walking Trails on the TV Mountain Sensitivity Analysis and Other Predictions The Mathematical Justification of Shadow Prices Sensitivity Analysis Column Generation Degeneracy Parametric Programming Networks Network Models Network Simplex Method Dijkstra's Algorithm for Shortest Paths Max Flow Min Cut Algorithms Hungarian Algorithm for Assignment as Primal-Dual Method Integrality and Duality Logarithmic Barrier and Other Interior-Point Methods Column Geometry of Simplex and Affine Scaling Algorithms Logarithmic Barrier and the Central Path Sparseness and Factorization Degeneracy, Crossover, and Other Considerations Advanced Topics on Polyhedra Polarity Separation Characterization of Convexity Polyhedral Cones Facets of Polyhedra Formulating and Solving Integer Programs Examples of IP Formulation Tighter Formulations Solving IPs Computational Complexity Introduction Complexity, and NP-Hardness The Straight Dope: Theory and Practice YES/NO Form The Nuts and Bolts of NP-Hardness Proofs Spotting Complexity Illustrations of Common Pitfalls Examples of NP-Hardness Proofs Dealing with NP-Hard Problems Other Complexity Classifications Conclusions and Recommended Reading Answers to Questions
Synopsis
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 textbook presents a theoretical treatment of linear programming, network flows and applications, integer programming, and computational complexity. The author includes a rigorous discussion of theory, numerous examples and exercises, and geometric intuitive explanations. He also offers computational tips and interpretation of software input. Unlike other books, this text incorporates duality throughout its chapters, rather than treating it as an add-on topic. It also discusses computational complexity theory, which can be used to classify problems according to the appropriate solution method.
LC Classification Number
T57.74

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