Linear and Integer Programming Vs Linear Integration and Counting: A Duality Viewpoint (Hardcover, 2009)

Preface. Introduction.- Part I. Linear Integration and Linear Programming. The Linear Integration Problem I. Comparing the Continuous Problems P and I.- Part II. Linear Counting and Integer Programming- The Linear Counting Problem 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.