Monographs on Discrete Mathematics and Applications 10
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.
The theory of discrete convex analysis has attracted the interest of many researchers in the field of optimization. Discrete Convex Analysis provides the information that professionals in optimization will need to “catch up” with this new theoretical development. It also presents an unexpected connection between matroid theory and mathematical economics and expounds a deeper connection between matrices and matroids than most standard textbooks. Professionals in areas other than optimization will enjoy applying these new mathematical techniques and ideas to their own problems.
List of Figures; Notation; Preface; Chapter 1: Introduction to the Central Concepts; Chapter 2: Convex Functions with Combinatorial Structures; Chapter 3: Convex Analysis, Linear Programming, and Integrality; Chapter 4: M-Convex Sets and Submodular Set Functions; Chapter 5: L-Convex Sets and Distance Functions; Chapter 6: M-Convex Functions; Chapter 7: L-Convex Functions; Chapter 8: Conjugacy and Duality; Chapter 9: Network Flows; Chapter 10: Algorithms; Chapter 11: Application to Mathematical Economics; Chapter 12: Application to Systems Analysis by Mixed Matrices; Bibliography; Index.
2003 / xxii + 389 pages / Softcover / ISBN-13: 978-1-611971-88-0
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