Linear programming: Foundations and extensions

Book Details

Author	Robert J. Vanderbei
Publisher	Springer
Year	2020 (5th Edition)
Language	English
Pages	471
Size	4.16 MB
Extension	PDF

Summary

Linear Programming: Foundations and Extensions by Robert J. Vanderbei is a comprehensive and authoritative textbook that serves as an introduction to the field of optimization[reference:0]. Now in its fifth edition, this book has become a cornerstone text in operations research and applied mathematics, renowned for its clear exposition, practical focus, and deep coverage of both theory and algorithms[reference:1].

The book begins with a substantial treatment of linear programming, developing the theory using problems expressed in inequality form rather than the more conventional equality form[reference:2]. It covers the fundamental simplex method, duality theory, and sensitivity analysis in detail[reference:3]. A unique and elegant feature of the book is its emphasis on the parametric self-dual simplex method, which is presented as a unifying theme throughout the text[reference:4][reference:5].

Beyond the basics, the book proceeds to convex analysis, network flows, integer programming, quadratic programming, and convex optimization[reference:6][reference:7]. It also touches on dynamic programming and the linear complementarity problem[reference:8]. The later chapters cover interior-point methods, a modern and powerful class of algorithms for solving large-scale optimization problems[reference:9]. The book also includes practical applications in areas such as game theory, regression, financial portfolio optimization, option pricing, and structural optimization[reference:10][reference:11].

The book is carefully written, with a focus on clarity and pedagogical effectiveness[reference:12]. Specific examples and concrete algorithms are presented before more abstract topics, making the material accessible[reference:13]. Numerous numerical examples are worked out in detail, and each chapter includes exercises that both illustrate the theory and, in some cases, extend it[reference:14]. The book comes with software that implements the major algorithms studied[reference:15].

Linear Programming: Foundations and Extensions is suitable for advanced undergraduate and master's level courses in linear programming, particularly in engineering, operations research, and mathematics departments[reference:16]. It is also an excellent reference for professionals and researchers, especially for those interested in interior-point methods and the computational aspects of linear programming[reference:17]. The fifth edition includes the latest theory and applications, ensuring that readers have access to the most up-to-date knowledge in the field[reference:18].

Key Features

• Comprehensive Coverage: Covers the full spectrum of linear programming, from the simplex method to interior-point methods, duality, sensitivity analysis, and extensions to convex, network, integer, and quadratic programming[reference:19].
• Parametric Self-Dual Simplex Method: A unique and elegant approach that unifies the presentation of the simplex method and provides a deep understanding of its theoretical foundations[reference:20].
• Inequality Form Focus: Develops the theory based on problems expressed in inequality form, a modern and practical approach that differs from traditional texts[reference:21].
• Practical Applications: Includes a wide range of business and non-business applications, such as resource allocation, blending, network flows, robust statistics, game theory, optimal design, portfolio optimization, and option pricing[reference:22].
• Pedagogical Excellence: Features a clear and accessible writing style, with specific examples and concrete algorithms preceding abstract topics[reference:23].
• Abundant Worked Examples: Numerous numerical examples are worked out in detail to illustrate the theory and algorithms[reference:24].
• Exercises and Extensions: Each chapter includes exercises that reinforce learning and, in some cases, extend the theory[reference:25].
• Accompanying Software: The book comes with software that implements the major algorithms, allowing readers to apply the techniques in practice[reference:26].
• Modern and Up-to-Date: The fifth edition includes the latest developments in optimization, ensuring that the content is current and relevant[reference:27].
• Versatile Audience: Suitable for advanced undergraduate and master's level courses, as well as a reference for professionals and researchers in optimization[reference:28].

About Author

Robert J. Vanderbei is a Professor in the Department of Operations Research and Financial Engineering at Princeton University[reference:29]. He served as the department chair from 2005 to 2012[reference:30]. He holds courtesy appointments in the Departments of Mathematics, Astrophysics, Computer Science, and Mechanical and Aerospace Engineering[reference:31]. He is also a member of the Program in Applied and Computational Mathematics, a founding member of the Bendheim Center for Finance, and a former Director of the Engineering and Management Systems Program[reference:32].

Professor Vanderbei is a Fellow of the American Mathematical Society (AMS), the Society for Industrial and Applied Mathematics (SIAM), and the Institute for Operations Research and the Management Sciences (INFORMS)[reference:33]. He has served as President of the INFORMS Optimization Society and the Computing Society[reference:34]. In 2017, he was awarded the prestigious Khachiyan Prize for his fundamental contributions to the field of optimization[reference:35][reference:36].

He holds degrees in Chemistry (BS), Operations Research and Statistics (MS), and Applied Mathematics (MS, PhD)[reference:37]. He received his PhD from Cornell University in 1981[reference:38]. After a postdoctoral fellowship at the Courant Institute of Mathematical Sciences (NYU) and a lectureship at the University of Illinois-Urbana/Champaign, he joined Bell Labs in 1984[reference:39]. At Bell Labs, he made fundamental contributions to optimization and holds three patents[reference:40]. In 1990, he joined Princeton University, where he has been since[reference:41].

In addition to hundreds of research papers, he has written four books, including the textbook Linear Programming: Foundations and Extensions, now in its fifth edition[reference:42]. He has also co-authored books on astronomy[reference:43].

Related Books

• Introduction to Operations Research - Frederick S. Hillier, Gerald J. Lieberman
• Nonlinear Programming: Theory and Algorithms - Mokhtar S. Bazaraa, Hanif D. Sherali, C. M. Shetty
• Linear Programming and Network Flows - Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali
• Convex Optimization - Stephen Boyd, Lieven Vandenberghe
• Integer Programming - Laurence A. Wolsey
• Network Flows: Theory, Algorithms, and Applications - Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin
• Nonlinear Optimization - Andrzej Ruszczynski
• Optimization in Operations Research - Ronald L. Rardin

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Frequently Asked Questions

Q: What is the main focus of this book?

A: The book focuses on linear programming and its extensions, providing a broad introduction to the theory and application of constrained optimization[reference:44].

Q: What is the parametric self-dual simplex method?

A: It is a unifying and elegant approach to the simplex method that is emphasized throughout the book, providing a deep understanding of the algorithm's theoretical foundations[reference:45].

Q: Is this book suitable for beginners?

A: Yes, it is designed as a first introduction to the topic, with specific examples and concrete algorithms preceding more abstract topics[reference:46]. It is suitable for advanced undergraduate and master's level courses[reference:47].

Q: Does the book include software?

A: Yes, the book comes with software that implements the major algorithms studied[reference:48].

Q: What applications are covered in the book?

A: The book covers a host of practical business applications (resource allocation, blending, network flows) as well as non-business applications such as robust statistics, game theory, optimal design, portfolio optimization, and option pricing[reference:49].

Q: What is the difference between this book and other linear programming textbooks?

A: This book develops the theory based on problems expressed in inequality form rather than the more conventional equality form[reference:50]. It also places a special emphasis on the parametric self-dual simplex method[reference:51].

Q: Is this book recommended for self-study?

A: Yes, it is highly recommended for both self-study and as teaching material[reference:52]. The clear explanations, numerous examples, and exercises make it ideal for independent learning.

Q: What is the academic level of this book?

A: It is appropriate for advanced undergraduate and master's level courses in linear programming, particularly in engineering, operations research, and mathematics[reference:53].