Description
Book SynopsisDiscrete 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.
Table of Contents
- 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.
