Description
Book Synopsis
1 Linear and Integer Linear Optimization.- 2 Linear Systems and Projection.- 3 Linear Systems and Inverse Projection.- 4 Integer Linear Systems: Projection and Inverse Projection.- 5 The Simplex Algorithm.- 6 More on Simplex.- 7 Interior Point Algorithms: Polyhedral Transformations.- 8 Interior Point Algorithms: Barrier Methods.- 9 Integer Programming.- 10 Projection: Benders' Decomposition.- 11 Inverse Projection: Dantzig-Wolfe Decomposition.- 12 Lagrangian Methods.- 13 Sparse Methods.- 14 Network Flow Linear Programs.- 15 Large Integer Programs: Preprocessing and Cutting Planes.- 16 Large Integer Programs: Projection and Inverse Projection.- VI Appendix.- A Polyhedral Theory.- A.1 Introduction.- A.2 Concepts and Definitions.- A.3 Faces of Polyhedra.- A.4 Finite Basis Theorems.- A.5 Inner Products, Subspaces and Orthogonal Subspaces.- A. 6 Exercises.- B Complexity Theory.- B.1 Introduction.- B.2 Solution Sizes.- B.3 The Turing Machine.- B.4 Complexity Classes.- B.5 Satisfiability.- B.
Trade Review
From the reviews of the first edition:
"This book is a very comprehensive textbook of linear and integer optimization. It presents a unified approach to the subject and is one of the few books treating linear and integer aspects together. … This is an interesting book with special features. … The text is written in a clear and readily comprehensible way, and it contains computer programs as well as many examples being helpful for students. This book is an important textbook of mathematical programming." (Johannes Jahn, Zentralblatt MATH, Vol. 1053 (4), 2005)
Table of Contents
Preface. Part I: Motivation. 1. Linear and Integer Linear Optimization. Part II: Theory. 2. Linear Systems and Projection. 3. Linear Systems and Inverse Projection. 4. Integer Linear Systems: Projection and Inverse Projection. Part III: Algorithms. 5. The Simplex Algorithm. 6. More on Simplex. 7. Interior Point Algorithms: Polyhedral Transformations. 8. Interior Point Algorithms: Barrier Methods. 9. Integer Programming. Part IV: Solving Large Scale Problems: Decomposition Methods. 10. Projection: Benders's Decomposition Methods. 11. Inverse Projection: Dantzig-Wolfe Decomposition. 12. Lagrangian Methods. Part V: Solving Large Scale Problems: Using Special Structure. 13. Sparse Methods. 14. Network Flow Linear Programs. 15. Large Integer Programs: Preprocessing and Cutting Planes. 16. Large Integer Programs: Projection and Inverse Projection. Part VI: Appendix. A. Polyhedral Theory. B. Complexity Theory. C. Basic Graph Theory. D. Software and Test Problems. E. Notation. Bibliography. References. Author Index. Topic Index.
