Linear and integer programming vs linear integration and counting: a duality viewpoint

This book analyzes and compares four closely related problems, namely linear programming, integer programming, linear integration, and linear summation (orcounting). The focus is on duality and the novel approach puts integer programming in perspective with three associated problems, and permits one to definediscrete analogues of well-known continuous duality concepts, and the rationale behind them. Also, the approach highlights the difference between the discrete and continuous cases. Central in the analysis are the continuous and discrete Brion and Vergne’s formulae for linear integration and counting which are not very well-known in the optimization community. This approach provides somenew insights on duality concepts for integer programs, and also permits to retrieve and shed new light on some well-known results. For instance, Gomory relaxations and the abstract superadditive dual of integer programs are re-interpreted in this algebraic approach. Analyzes and compares four closely related nontrivial problems, namely linear programming, integer programming, linear integration, linear summation (or counting) with a focus on duality Provides somenew insights on duality concepts for integer programs, and also permits to retrieve and shed new light on some well-known results INDICE: Preface. Introduction.- Part I. Linear Integration and Linear Programming. The Linear Integration Problem I. Comparing the Continuous Problems Pand I.- Part II. Linear Counting and Integer Programming- The Linear CountingProblem I(d). Relating the Discrete Problems P(d) and I(d) with P.- Part III.Duality. Duality and Gomory Relaxations. Barvinok’s Counting Algorithm and Gomory Relaxations. A Discrete Farkas Lemma. The Integer Hull of a Convex Rational Polytope. Duality and Superadditive Functions.- Appendix: Legendre-Fenchel,Laplace, Cramer, and Z Transforms. References. Glossary.- Index.

• ISBN: 978-0-387-09413-7
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 200
• Fecha Publicación: 01/04/2009
• Nº Volúmenes: 1
• Idioma: Inglés