http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
"Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis."--Jacket.
1. Introduction to the Central Concepts -- 2. Convex Functions with Combinatorial Structures -- 3. Convex Analysis, Linear Programming, and Integrality -- 4. M-Convex Sets and Submodular Set Functions -- 5. L-Convex Sets and Distance Functions -- 6. M-Convex Functions -- 7. L-Convex Functions -- 8. Conjugacy and Duality -- 9. Network Flows -- 10. Algorithms -- 11. Application to Mathematical Economics -- 12. Application to Systems Analysis by Mixed Matrices.
Includes bibliographical references (pages 363-377) and index.
SIAM monographs on discrete mathematics and applications