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

Dimitris Alevras (Author), Manfred W. Padberg (Author)

Book Description

Publication Date: June 27, 2001 | Series: Universitext

This book offers a comprehensive treatment of the exercises and case studies as well as summaries of the chapters of the book "Linear Optimization and Extensions" by Manfred Padberg. It covers the areas of linear programming and the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces.
Here are the main topics treated in the book: Simplex algorithms and their derivatives including the duality theory of linear programming. Polyhedral theory, pointwise and linear descriptions of polyhedra, double description algorithms, Gaussian elimination with and without division, the complexity of simplex steps. Projective algorithms, the geometry of projective algorithms, Newtonian barrier methods. Ellipsoids algorithms in perfect and in finite precision arithmetic, the equivalence of linear optimization and polyhedral separation. The foundations of mixed-integer programming and combinatorial optimization.

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 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 Best Sellers Rank: #2,485,017 in Books (See Top 100 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).