Understanding and Using Linear Programming (Universitext)

This is an introductory textbook of linear programming, written mainly for students of computer science and mathematics. Our guiding phrase is, “what everytheoreticalcomputerscientistshouldknowaboutlinearprogramming.” The book is relatively concise, in order to allow the reader to focus on the basic ideas. For a number of topics commonly appearing in thicker books on the subject, we were seriously tempted to add them to the main text, but we decided to present them only very brie?y in a separate glossary. At the same time, we aim at covering the main results with complete proofs and in su?cient detail, in a way ready for presentation in class. One of the main focuses is applications of linear programming, both in practice and in theory. Linear programming has become an extremely ?- ible tool in theoretical computer science and in mathematics. While many of the ?nest modern applications are much too complicated to be included in an introductory text, we hope to communicate some of the ?avor (and excitement) of such applications on simpler examples. This is an introductory textbook of linear programming, written mainly for students of computer science and mathematics. Our guiding phrase is,'what every theoretical computer scientist should know about linear programming'. The book is relatively concise, in order to allow the reader to focus on the basic ideas. For a number of topics commonly appearing in thicker books on the subject, we were seriously tempted to add them to the main text, but we decided to present them only very brie?y in a separate glossary. At the same time, we aim at covering the main results with complete proofs and in su?cient detail, in a way ready for presentation in class. One of the main focuses is applications of linear programming, both in practice and in theory. Linear programming has become an extremely?- ible tool in theoretical computer science and in mathematics. While many of the?nest modern applications are much too complicated to be included in an introductory text, we hope to communicatesome of the?avor (and excitement) of such applications on simpler examples.

the Book Is An Introductory Textbook Mainly For Students Of Computer Science And Mathematics. Our Guiding Phrase Is What Every Theoretical Computer Scientist Should Know About Linear Programming. A Major Focus Is On Applications Of Linear Programming, Both In Practice And In Theory. The Book Is Concise, But At The Same Time, The Main Results Are Covered With Complete Proofs And In Sufficient Detail, Ready For Presentation In Class. The Book Does Not Require More Prerequisites Than Basic Linear Algebra, Which Is Summarized In An Appendix. One Of Its Main Goals Is To Help The Reader To See Linear Programming Behind The Scenes.

Front Matter....Pages I-VIII What Is It, and What For?....Pages 1-10 Examples....Pages 11-27 Integer Programming and LP Relaxation....Pages 29-40 Theory of Linear Programming: First Steps....Pages 41-56 The Simplex Method....Pages 57-79 Duality of Linear Programming....Pages 81-104 Not Only the Simplex Method....Pages 105-130 More Applications....Pages 131-191 Software and Further Reading....Pages 193-193 Back Matter....Pages 195-226 Linear programming, surprisingly, is not directly related to computer programming.