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Discrete convex analysis

Author: Kazuo Murota
Publisher: Philadelphia : Society for Industrial and Applied Mathematics, ©2003.
Series: SIAM monographs on discrete mathematics and applications.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Murota, Kazuo, 1955-
Discrete convex analysis.
Philadelphia : Society for Industrial and Applied Mathematics, ©2003
(DLC) 2003042468
(OCoLC)51559058
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Kazuo Murota
ISBN: 0898715407 9780898715408 9780898718508 0898718503
OCLC Number: 694086053
Description: xxii, 389 pages : illustrations ; 27 cm.
Contents: Introduction to the Central Concepts --
Convex Functions with Combinatorial Structures --
Convex Analysis, Linear Programming, and Integrality --
M-Convex Sets and Submodular Set Functions --
L-Convex Sets and Distance Functions --
M-Convex Functions --
L-Convex Functions --
Conjugacy and Duality --
Network Flows --
Algorithms --
Application to Mathematical Economics --
Application to Systems Analysis by Mixed Matrices.
Series Title: SIAM monographs on discrete mathematics and applications.
Responsibility: Kazuo Murota.

Abstract:

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.

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