Connections In Combinatorial Optimization
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Connections In Combinatorial Optimization
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Author : András Frank
language : en
Publisher: OUP Oxford
Release Date : 2011-02-24
Connections In Combinatorial Optimization written by András Frank and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-24 with Mathematics categories.
Filling the gap between introductory and encyclopedic treatments, this book provides rich and appealing material for a second course in combinatorial optimization. This book is suitable for graduate students as well as a reference for established researchers.
Combinatorial Optimization
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Author : Bernhard Korte
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-27
Combinatorial Optimization written by Bernhard Korte 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 2006-01-27 with Mathematics categories.
This well-written textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete (but concise) proofs, as well as many deep results, some of which have not appeared in any previous books.
Polyhedral And Semidefinite Programming Methods In Combinatorial Optimization
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Author : Levent Tunçel
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-05-05
Polyhedral And Semidefinite Programming Methods In Combinatorial Optimization written by Levent Tunçel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with categories.
Since the early 1960s, polyhedral methods have played a central role in both the theory and practice of combinatorial optimization. Since the early 1990s, a new technique, semidefinite programming, has been increasingly applied to some combinatorial optimization problems. The semidefinite programming problem is the problem of optimizing a linear function of matrix variables, subject to finitely many linear inequalities and the positive semidefiniteness condition on some of the matrix variables. On certain problems, such as maximum cut, maximum satisfiability, maximum stable set and geometric representations of graphs, semidefinite programming techniques yield important new results. This monograph provides the necessary background to work with semidefinite optimization techniques, usually by drawing parallels to the development of polyhedral techniques and with a special focus on combinatorial optimization, graph theory and lift-and-project methods. It allows the reader to rigorously develop the necessary knowledge, tools and skills to work in the area that is at the intersection of combinatorial optimization and semidefinite optimization. A solid background in mathematics at the undergraduate level and some exposure to linear optimization are required. Some familiarity with computational complexity theory and the analysis of algorithms would be helpful. Readers with these prerequisites will appreciate the important open problems and exciting new directions as well as new connections to other areas in mathematical sciences that the book provides.
Generalized Network Design Problems
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Author : Petrica C. Pop
language : en
Publisher: Walter de Gruyter
Release Date : 2012-10-30
Generalized Network Design Problems written by Petrica C. Pop and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.
Combinatorial optimization is a fascinating topic. Combinatorial optimization problems arise in a wide variety of important fields such as transportation, telecommunications, computer networking, location, planning, distribution problems, etc. Important and significant results have been obtained on the theory, algorithms and applications over the last few decades. In combinatorial optimization, many network design problems can be generalized in a natural way by considering a related problem on a clustered graph, where the original problem's feasibility constraints are expressed in terms of the clusters, i.e., node sets instead of individual nodes. This class of problems is usually referred to as generalized network design problems (GNDPs) or generalized combinatorial optimization problems. The express purpose of this monograph is to describe a series of mathematical models, methods, propositions, algorithms developed in the last years on generalized network design problems in a unified manner. The book consists of seven chapters, where in addition to an introductory chapter, the following generalized network design problems are formulated and examined: the generalized minimum spanning tree problem, the generalized traveling salesman problem, the railway traveling salesman problem, the generalized vehicle routing problem, the generalized fixed-charge network design problem and the generalized minimum vertex-biconnected network problem. The book will be useful for researchers, practitioners, and graduate students in operations research, optimization, applied mathematics and computer science. Due to the substantial practical importance of some presented problems, researchers in other areas will find this book useful, too.
Simulated Annealing And Boltzmann Machines
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Author : Emile H. L. Aarts
language : en
Publisher: John Wiley & Sons
Release Date : 1989
Simulated Annealing And Boltzmann Machines written by Emile H. L. Aarts and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Computers categories.
Wiley-Interscience Series in Discrete Mathematics and Optimization Advisory Editors Ronald L. Graham Jan Karel Lenstra Robert E. Tarjan Discrete Mathematics and Optimization involves the study of finite structures. It is one of the fastest growing areas in mathematics today. The level and depth of recent advances in the area and the wide applicability of its evolving techniques point to the rapidity with which the field is moving from its beginnings to maturity and presage the ever-increasing interaction between it and computer science. The Series provides a broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, mathematical programming and the analysis of algorithms, and including such topics as Ramsey theory, transversal theory, block designs, finite geometries, Polya theory, graph and matroid algorithms, network flows, polyhedral combinatorics and computational complexity. The Wiley - Interscience Series in Discrete Mathematics and Optimization will be a substantial part of the record of this extraordinary development. Recent titles in the Series: Search Problems Rudolf Ahlswede, University of Bielefeld, Federal Republic of Germany Ingo Wegener, Johann Wolfgang Goethe University, Frankfurt, Federal Republic of Germany The problems of search, exploration, discovery and identification are of key importance in a wide variety of applications. This book will be of great interest to all those concerned with searching, sorting, information processing, design of experiments and optimal allocation of resources. 1987 Introduction to Optimization E. M. L. Beale FRS, Scicon Ltd, Milton Keynes, and Imperial College, London This book is intended as an introduction to the many topics covered by the term 'optimization', with special emphasis on applications in industry. It is divided into three parts. The first part covers unconstrained optimization, the second describes the methods used to solve linear programming problems, and the third covers nonlinear programming, integer programming and dynamic programming. The book is intended for senior undergraduate and graduate students studying optimization as part of a course in mathematics, computer science or engineering. 1988
Geometric Algorithms And Combinatorial Optimization
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Author : Martin Grötschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Algorithms And Combinatorial Optimization written by Martin Grötschel 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 2012-12-06 with Mathematics categories.
Historically, there is a close connection between geometry and optImization. This is illustrated by methods like the gradient method and the simplex method, which are associated with clear geometric pictures. In combinatorial optimization, however, many of the strongest and most frequently used algorithms are based on the discrete structure of the problems: the greedy algorithm, shortest path and alternating path methods, branch-and-bound, etc. In the last several years geometric methods, in particular polyhedral combinatorics, have played a more and more profound role in combinatorial optimization as well. Our book discusses two recent geometric algorithms that have turned out to have particularly interesting consequences in combinatorial optimization, at least from a theoretical point of view. These algorithms are able to utilize the rich body of results in polyhedral combinatorics. The first of these algorithms is the ellipsoid method, developed for nonlinear programming by N. Z. Shor, D. B. Yudin, and A. S. NemirovskiI. It was a great surprise when L. G. Khachiyan showed that this method can be adapted to solve linear programs in polynomial time, thus solving an important open theoretical problem. While the ellipsoid method has not proved to be competitive with the simplex method in practice, it does have some features which make it particularly suited for the purposes of combinatorial optimization. The second algorithm we discuss finds its roots in the classical "geometry of numbers", developed by Minkowski. This method has had traditionally deep applications in number theory, in particular in diophantine approximation.
Combinatorial Optimization
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Author : Eugene L. Lawler
language : en
Publisher: Courier Corporation
Release Date : 2001-01-01
Combinatorial Optimization written by Eugene L. Lawler and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Perceptive text examines shortest paths, network flows, bipartite and nonbipartite matching, matroids and the greedy algorithm, matroid intersections, and the matroid parity problems. Suitable for courses in combinatorial computing and concrete computational complexity.
Handbook Of Combinatorial Optimization
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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-18
Handbook Of Combinatorial Optimization written by Ding-Zhu Du 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 2006-08-18 with Business & Economics categories.
This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.
Combinatorial Optimization
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Author : William J. Cook
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-30
Combinatorial Optimization written by William J. Cook and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-30 with Mathematics categories.
A complete, highly accessible introduction to one of today's most exciting areas of applied mathematics One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms. Because of its success in solving difficult problems in areas from telecommunications to VLSI, from product distribution to airline crew scheduling, the field has seen a ground swell of activity over the past decade. Combinatorial Optimization is an ideal introduction to this mathematical discipline for advanced undergraduates and graduate students of discrete mathematics, computer science, and operations research. Written by a team of recognized experts, the text offers a thorough, highly accessible treatment of both classical concepts and recent results. The topics include: * Network flow problems * Optimal matching * Integrality of polyhedra * Matroids * NP-completeness Featuring logical and consistent exposition, clear explanations of basic and advanced concepts, many real-world examples, and helpful, skill-building exercises, Combinatorial Optimization is certain to become the standard text in the field for many years to come.
Geometry Of Cuts And Metrics
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Author : Michel Marie Deza
language : en
Publisher: Springer
Release Date : 2009-11-12
Geometry Of Cuts And Metrics written by Michel Marie Deza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-12 with Mathematics categories.
Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.