Linear Optimization and Extensions: Problems and Solutions (Universitext) (Paperback)

by Dimitris Alevras (Author), Manfred W. Padberg (Author) "(i) To formulate LLI's problem denote by x1 the liters of bourbon and by x2 the liters of whiskey produced during the planning period..." (more)
Key Phrases: double description algorithm, linear optimization problem max, airlift model, Variable Variable Description Enthalpy, Operation Fiddle, Joe Doe (more...)

Editorial Reviews

Review
From the reviews of the first edition: "... This book is a useful supplement to the textbook [W.Padberg, Linear Optimization and Extensions, 2nd ed., Springer, Berlin 1999]. It serves the purpose well to train MATHEMATICAL optimizers, but has little impact on the education of mathematical OPTIMIZERS, i.e. it concentrates on mathematics, but not on problem solving in reality. It is a valuable contribution for students in mathematics, but may be less suitable for students of economics or business administration." OR-Spektrum, Issue 14, p.37, 2002  "Die in diesem Werk präsentierten Übungsaufgaben wurden überarbeitet, ergänzt, und werden im vorliegenden Text samt Lösungen und geraffter Zusammenfassung der notwendigen theoretischen Resultate präsentiert. ... Bemerkenswert ist weiters, daß auch Programmieraufgaben gestellt und gelöst werden. ... Insgesamt ist das Buch sowohl als Quelle für Übungsaufgaben zu Vorlesungen über Lineare Optimierung als auch zum Selbststudieum sehr gut geeignet." F.Rendl (Klagenfurt), IMN - Internationale Mathematische Nachrichten 190, 2002, S. 76-77 "Do you know M. Padberg’s Linear Optimization and Extensions (second edition, Springer-Verlag, Berlin, 1999)? If you teach a course on linear programming then you should know it. ... Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. … For those who cherish the original textbook (students and lecturers) this is an extremely valuable sequel. For those who strive for good exercises and case studies for LP this is an excellent volume." (Péter Hajnal, Acta Scientiarum Mathematicarum, Vol.69, 2003)

Product Description
Offers a comprehensive treatment of the exercises and case studies. Covers the areas of linear programming and the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces. Softcover.

Product Details

• Paperback: 453 pages
• Publisher: Springer; 1 edition (June 27, 2001)
• Language: English
• ISBN-10: 3540417443
• ISBN-13: 978-3540417446
• Product Dimensions: 9.5 x 7.6 x 1 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #1,123,604 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

4.0 out of 5 stars A good reference for Linear Programming Theory, June 1, 2000

By A Customer

This review is from: Linear Optimization and Extensions (Algorithms and Combinatorics) (Hardcover)

This book is certainly a very good reference for theoretical topics of linear programming. It covers the Simplex method and the Ellipsoid algorithms. It also covers the geometry of linear programming (polyhedra and polytopes, etc). It certainly covers more topics than most other linear programming texts. As expected, a book writen for theoretical topics is certainly not easy to read, especially for people with no training in doing rigorous mathematical proofs. Also, not many examples or illustrations are given in this book, and this might be a problem for some readers.

3 of 3 people found the following review helpful:

5.0 out of 5 stars Computational and Mathematical Excellence, May 26, 2002

By	Mathematical Statistician with Social Interests (Uppsala, Ohio) - See all my reviews

This review is from: Linear Optimization and Extensions (Algorithms and Combinatorics) (Hardcover)

For nearly 30 years, Padberg has been a leader in computational integer programming and in combinatorial optimization theory.

In practice, Padberg has helped to design and implement "branch-and-cut" methods for finding exact optimal solutions to large traveling salesman problems, and this approach is a method of choice for finding approximately optimal solutions to tough industrial problems. The book provides the mathematical and computational background for understanding branch-and-cut; the established mathematical texts by Nemhauser and Wolsey and by Schrijver are less detailed and more condensed, and omit numerical issues. The treatment of modern simplex algorithms for linear programming---updating LU factorizations and using column- and constraint-generation and -purging---is excellent, and a large bibliography contains recent references. Besides industrial and Berlin-airlift scheduling problems, the book contains TSP examples of circuit-board wiring, U.S. state capitals, and Odysseus!

Three more highlights: The double description algorithm receives a complete description, and this is useful for combinatorial geometers. The discussion of integer-arithmetic and complexity theory is very readable, and these technical topics are slighted by interior-point books (besides Wright's quickie), despite their importance in integer programming and combinatorial optimization. The discussion of interior-point algorithms emphasizes projective geometry, a beautiful theory that has inspired so much of optimization theory---besides Karmarkar's interior-point algorithm, Dantzig's simplex algorithm, Fenchel duality, Davidon's conic algorithm for nonlinear optimization, etc.).

The book is not a comprehensive survey of linear programming,
and lacks a treatment of Nesterov's theory of self-concordant barrier-functions. Also, no treatment is given of pivoting algorithms besides Dantzig's (e.g., Terlaky's criss-cross method, Todd's oriented matroid algorithm).