Discrete Convex Analysis

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SIAM, 2003 - Mathematics - 389 pages
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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. 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.
  

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Contents

Convex Functions with Combinatorial Structures
39
Convex Analysis Linear Programming and Integrality
77
Conjugacy and Duality
205
Network Flows
245
Algorithms
281
Application to Mathematical Economics
323
Application to Systems Analysis by Mixed Matrices
347
Bibliography
363
Index
379
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Page 375 - DD Siljak, Large-Scale Dynamic Systems: Stability and Structure (North-Holland, New York, 1978).

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Algorithms in Discrete Convex Analysis (researchindex)
This is a survey of algorithmic results in the theory of discrete convex analysis for integer valued functions defined on integer lattice points.
citeseer.ist.psu.edu/ 209185.html

Science Links Japan | Discrete Optimization Algorithms based on ...
Abstract;The leader of this research group proposed a theoretical system called "discrete convex analysis" in recent years as an attempt for viewing ...
sciencelinks.jp/ j-east/ article/ 200402/ 000020040203A0734672.php

Discrete convex analysis
A theory of "discrete convex analysis" is developed for integer-valued functions ... "discrete convex analysis". To be specific, we give a Lagrange duality ...
www.springerlink.com/ index/ G1Q1U3571145151X.pdf

Introduction to the Central Concepts
“Discrete Convex Analysis” aims at establishing a new theoretical ... The motive for “Discrete Convex Analysis” is explained in general terms of opti- ...
www.misojiro.t.u-tokyo.ac.jp/ ~murota/ mybooks/ DCAsiamaimhistory.pdf

DROPS - Document
This talk describes fundamental properties of M-convex and L-convex functions that play the central roles in discrete convex analysis. ...
drops.dagstuhl.de/ opus/ frontdoor.php?source_opus=216

Discrete convex analysis
Satoru Fujishige , Akihisa Tamura, A Two-Sided Discrete-Concave Market with Possibly Bounded Side Payments: An Approach by Discrete Convex Analysis, ...
portal.acm.org/ citation.cfm?id=303269& dl=GUIDE& coll=GUIDE& CFID=15151515& CFTOKEN=6184618

Discrete Convex Analysis - Cambridge University Press
Discrete Convex Analysis, Kazuo Murota, 9780898715408, Cambridge University Press.
www.cambridge.org/ us/ catalogue/ catalogue.asp?isbn=0898715407

Satoru Iwata
Discrete Convex Analysis. A Capacity Scaling Algorithm for M-Convex Submodular Flow (with S. Moriguchi, K. Murota), Math. Programming, 103 (2005), 181-202. ...
www.kurims.kyoto-u.ac.jp/ ~iwata/

Selected publications of K. Murota
K. Murota (2003): Discrete Convex Analysis. SIAM Monographs on Discrete ... K. Murota (1998): Discrete convex analysis, Mathematical Programming, 83, ...
www.misojiro.t.u-tokyo.ac.jp/ ~murota/ publist.html

Discrete convex analysis , by Kazuo Murota, SIAM Monographs on ...
The author writes in the preface: “Discrete Convex Analysis is aimed at estab- ... (the name “discrete convex analysis” was, apparently, coined by the ...
www.ams.org/ bull/ 2004-41-03/ S0273-0979-04-01015-8/ S0273-0979-04-01015-8.pdf

About the author (2003)

Murota is a Professor in the Department of Mathematical Informatics, Graduate School of Information Science and Technology, at the University of Tokyo.

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