
Discrete Convex Analysis
Kazuo Murota(Author)
Society for Industrial & Applied Mathematics,U.S. (Publisher)
Published on 30. July 2013
Book
Paperback/Softback
411 pages
978-1-61197-255-9 (ISBN)
Description
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.
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.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Dimensions
Height: 229 mm
Width: 152 mm
Weight
733 gr
ISBN-13
978-1-61197-255-9 (9781611972559)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
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.
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.