Linear Optimization and Duality

A Modern Exposition

Craig A. Tovey (Georgia Institute of Technology, Atlanta, USA)

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English

Chapman & Hall/CRC
26 August 2024

Product design; Probability & statistics; Optimisation; Engineering: general; Computer science

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.

By: Craig A. Tovey (Georgia Institute of Technology Atlanta USA)
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm,
Weight: 1.080kg
ISBN: 9780367618209
ISBN 10: 0367618206
Pages: 586
Publication Date: 26 August 2024
Audience: College/higher education , Primary
Format: Paperback
Publisher's Status: Active

Introduction. Formulating and Solving Linear Programs. Polyhedra. The Simplex Method and Its Variants. The Geography of Mount Duality. Sensitivity Analysis and Other Predictions. Networks. Logarithmic Barrier and Other Interior-Point Methods. Advanced Topics on Polyhedra. Formulating and Solving Integer Programs. Computational Complexity. Conclusions and Recommended Reading. Answers to Questions.

Craig A. Tovey is a professor at Georgia Tech. Institute.