Linear Optimization and Extensions

I was pleasantly surprised when I was asked by Springer-Verlag to prepare a second edition of this volume on Linear Optimization and Extensions, which - not exactly contrary to my personal expectations - has apparently been accepted reasonably weIl by the global optimization community. My objective in putting this book together was originally - and still is - to detail the major algorithmic ideas in linear optimization that have evolved in the past fifty years or so and that have changed the historical optimization "landscape" in substantial ways - both theoretically and computationally. While I may have overlooked the importance of some very recent developments - the work by Farid Alizadeh which generalizes linear programming to "sem i-definite" programming is perhaps a candidate for one of my omissions - I think that major new breakthraughs on those two fronts that interest me - theory and computation - have not occurred since this book was published originally. As a consequence I have restricted myself to a thorough re-working of the original manuscript with the goal of making it more readable. Of course, I have taken this opportunity to correct a few "Schönheitsfehler" of the first edition and to add some illustrations. The index to this volume has been extended substantially - to permit a hurried reader a quicker glance at the wealth of topics that were covered nevertheless already in the first edition. As was the case with the first edition, Dr.

The book is one of the few available graduate textbooks on linear optimisation Includes supplementary material: sn.pub/extras

Résumé

From the reviews of the second edition:

"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. It is a successful book on LP with many application driven exercises. Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. Tell your student about it. ...

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

"Linear Optimization and Extensions - Problems and Solutions - is a solution manual for another book, released in 2000 ... . The book is a very well planned and written. ... For professors and interested students, the book can also serve as a source of advanced exercises. ... the book will prove invaluable not only for students, but also for professionals in industry and universities. This is certainly an important addition to the literature of the area of linear programming." (Carlos Oliveria, SIGACT News, Vol. 35 (4), 2004)

Contenu
The Linear Programming Problem.- Basic Concepts.- Five Preliminaries.- Simplex Algorithms.- Primal-Dual Pairs.- Analytical Geometry.- Projective Algorithms.- Ellipsoid Algorithms.- Combinatorial Optimization: An Introduction.