Discrete Convex Analysis

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Discrete Convex Analysis

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Author : Kazuo Murota
language : en
Publisher:
Release Date : 2003

Discrete Convex Analysis written by Kazuo Murota and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.

Discrete Convex Analysis

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Author : Kazuo Murota
language : en
Publisher:
Release Date : 1996

Discrete Convex Analysis written by Kazuo Murota and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Combinatorial optimization categories.

Abstract: "This is a survey of the theory of 'discrete convex analysis' that has been developed recently by the author for integer-valued functions defined on integer lattice points. The theory parallels the ordinary convex analysis, covering discrete analogues of the fundamental concepts such as conjugacy, subgradients, the Fenchel min-max duality, and separation theorems. The technical development is based on matroid- theoretic concepts, in particular, submodular functions and exchange axioms. The results extend the relationship investigated in the eighties between convex functions and submodular functions. This paper puts stress on conjugacy and duality for discrete convex functions."

Research Trends In Combinatorial Optimization

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Author : William J. Cook
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-07

Research Trends In Combinatorial Optimization written by William J. Cook and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-07 with Mathematics categories.

The editors and authors dedicate this book to Bernhard Korte on the occasion of his seventieth birthday. We, the editors, are happy about the overwhelming feedback to our initiative to honor him with this book and with a workshop in Bonn on November 3–7,2008.Althoughthiswouldbeareasontolookback,wewouldratherliketolook forward and see what are the interesting research directions today. This book is written by leading experts in combinatorial optimization. All - pers were carefully reviewed, and eventually twenty-three of the invited papers were accepted for this book. The breadth of topics is typical for the eld: combinatorial optimization builds bridges between areas like combinatorics and graph theory, submodular functions and matroids, network ows and connectivity, approximation algorithms and mat- matical programming, computational geometry and polyhedral combinatorics. All these topics are related, and they are all addressed in this book. Combi- torial optimization is also known for its numerous applications. To limit the scope, however, this book is not primarily about applications, although some are mentioned at various places. Most papers in this volume are surveys that provide an excellent overview of an activeresearcharea,butthisbookalsocontainsmanynewresults.Highlightingmany of the currently most interesting research directions in combinatorial optimization, we hope that this book constitutes a good basis for future research in these areas.

Discrete Convex Analysis And Its Applications In Operations

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Author : Xin Chen
language : en
Publisher:
Release Date : 2020

Discrete Convex Analysis And Its Applications In Operations written by Xin Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.

Discrete convexity, in particular, L-natural-convexity and M-natural-convexity, provides a critical opening to attack several classical problems in inventory theory, as well as many other operations problems that arise from more recent practices, for instance, appointment scheduling and bike-sharing. As a powerful framework, discrete convex analysis is becoming increasingly popular in the literature. This review will survey the landscape of the approach. We start by introducing several key concepts, namely, L-natural-convexity and M-natural-convexity and their variants, followed by a discussion of some fundamental properties that are most useful for studying operations models. We then illustrate various applications of these concepts and properties. Examples include network flow problem, stochastic inventory control, appointment scheduling, game theory, portfolio contract, discrete choice model, and bike-sharing. We focus our discussion on demonstrating how discrete convex analysis can shed new insights on existing problems, and/or bring about much simpler analyses and algorithm developments than previous methods in the literature. We also present several results and analyses that are new to the literature.

Submodular Functions And Optimization

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Author : Satoru Fujishige
language : en
Publisher: Elsevier
Release Date : 2005-07-26

Submodular Functions And Optimization written by Satoru Fujishige and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-26 with Mathematics categories.

It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics. - Self-contained exposition of the theory of submodular functions - Selected up-to-date materials substantial to future developments - Polyhedral description of Discrete Convex Analysis - Full description of submodular function minimization algorithms - Effective insertion of figures - Useful in applied mathematics, operations research, computer science, and economics

Recent Developments In Discrete Convex Analysis

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Author :
language : en
Publisher:
Release Date : 2008

Recent Developments In Discrete Convex Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Algorithms In Discrete Convex Analysis

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Author : Kazuo Murota
language : en
Publisher:
Release Date : 1999

Algorithms In Discrete Convex Analysis written by Kazuo Murota and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Lattice theory categories.

Abstract: "This is a survey of algorithmic results in the theory of 'discrete convex analysis' for integer-valued functions defined on integer lattice points. The theory parallels the ordinary convex analysis, covering discrete analogues of the fundamental concepts such as conjugacy, the Fenchel min-max duality, and separation theorems. The thechnical development is based on matriod-theoretic concepts, in particular, submodular functions and exchange axioms."

Combinatorial Optimization And Graph Algorithms

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Author : Takuro Fukunaga
language : en
Publisher: Springer
Release Date : 2017-10-02

Combinatorial Optimization And Graph Algorithms written by Takuro Fukunaga and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-02 with Computers categories.

Covering network designs, discrete convex analysis, facility location and clustering problems, matching games, and parameterized complexity, this book discusses theoretical aspects of combinatorial optimization and graph algorithms. Contributions are by renowned researchers who attended NII Shonan meetings on this essential topic. The collection contained here provides readers with the outcome of the authors’ research and productive meetings on this dynamic area, ranging from computer science and mathematics to operations research. Networks are ubiquitous in today's world: the Web, online social networks, and search-and-query click logs can lead to a graph that consists of vertices and edges. Such networks are growing so fast that it is essential to design algorithms to work for these large networks. Graph algorithms comprise an area in computer science that works to design efficient algorithms for networks. Here one can work on theoretical or practical problems where implementation of an algorithm for large networks is needed. In two of the chapters, recent results in graph matching games and fixed parameter tractability are surveyed. Combinatorial optimization is an intersection of operations research and mathematics, especially discrete mathematics, which deals with new questions and new problems, attempting to find an optimum object from a finite set of objects. Most problems in combinatorial optimization are not tractable (i.e., NP-hard). Therefore it is necessary to design an approximation algorithm for them. To tackle these problems requires the development and combination of ideas and techniques from diverse mathematical areas including complexity theory, algorithm theory, and matroids as well as graph theory, combinatorics, convex and nonlinear optimization, and discrete and convex geometry. Overall, the book presents recent progress in facility location, network design, and discrete convex analysis.

Experimental Algorithms

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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-28

Experimental Algorithms written by Panos M. Pardalos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-28 with Computers categories.

This volume constitutes the refereed proceedings of the 10th International Symposium on Experimental Algorithms, SEA 2011, held in Kolimpari, Chania, Crete, Greece, in May 2011. The 36 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 83 submissions and present current research in the area of design, analysis, and experimental evaluation and engineering of algorithms, as well as in various aspects of computational optimization and its applications.

Integer Programming And Combinatorial Optimization

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Author : William J. Cook
language : en
Publisher: Springer
Release Date : 2003-08-01

Integer Programming And Combinatorial Optimization written by William J. Cook and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-01 with Computers categories.

This volume contains the papers selected for presentation at IPCO 2002, the NinthInternationalConferenceonIntegerProgrammingandCombinatorial- timization, Cambridge, MA (USA), May 27–29, 2002. The IPCO series of c- ferences highlights recent developments in theory, computation, and application of integer programming and combinatorial optimization. IPCO was established in 1988 when the ?rst IPCO program committee was formed. IPCO is held every year in which no International Symposium on Ma- ematical Programming (ISMP) takes places. The ISMP is triennial, so IPCO conferences are held twice in every three-year period. The eight previous IPCO conferences were held in Waterloo (Canada) 1990, Pittsburgh (USA) 1992, Erice (Italy) 1993, Copenhagen (Denmark) 1995, Vancouver (Canada) 1996, Houston (USA) 1998, Graz (Austria) 1999, and Utrecht (The Netherlands) 2001. In response to the call for papers for IPCO 2002, the program committee received 110 submissions, a record number for IPCO. The program committee met on January 7 and 8, 2002, in Aussois (France), and selected 33 papers for inclusion in the scienti?c program of IPCO 2002. The selection was based on originality and quality, and re?ects many of the current directions in integer programming and combinatorial optimization research.