## Discrete Convex AnalysisDiscrete 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 |

363 | |

379 | |

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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&

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