Iterative Methods In Combinatorial Optimization

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Iterative Methods in Combinatorial Optimization

Author : Lap Chi Lau
Publisher : Cambridge University Press
ISBN 13 : 1139499394
Total Pages : 255 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Iterative Methods in Combinatorial Optimization by : Lap Chi Lau

Download or read book Iterative Methods in Combinatorial Optimization written by Lap Chi Lau and published by Cambridge University Press. This book was released on 2011-04-18 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.

Iterative Methods, Combinatorial Optimization, and Linear Programming Beyond the Universal Barrier

Author : Aaron Daniel Sidford
Publisher :
ISBN 13 :
Total Pages : 266 pages
Book Rating : 4.:/5 (927 download)

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Book Synopsis Iterative Methods, Combinatorial Optimization, and Linear Programming Beyond the Universal Barrier by : Aaron Daniel Sidford

Download or read book Iterative Methods, Combinatorial Optimization, and Linear Programming Beyond the Universal Barrier written by Aaron Daniel Sidford and published by . This book was released on 2015 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we consider fundamental problems in continuous and combinatorial optimization that occur pervasively in practice and show how to improve upon the best known theoretical running times for solving these problems across a broad range of parameters. Using and improving techniques from diverse disciplines including spectral graph theory, numerical analysis, data structures, and convex optimization we provide the first theoretical improvements in decades for multiple classic problems ranging from linear programming to linear system solving to maximum flow. Key results in this thesis include the following: -- Linear Programming: We provide the first general improvement to both the running time and convergence rate of polynomial time algorithms for solving linear programs in over 15 years. For a linear program with constraint matrix A, with z nonzero entries, and bit complexity L our algorithm runs in time [mathematical formula] -- Directed Maximum Flow: We provide an [mathematical formula] time algorithm for solving the-maximum flow problem on directed graphs with m edges, n vertices, and capacity ratio U improving upon the running time of [mathematical formula] achieved over 15 years ago by Goldberg and Rao. -- Undirected Approximate Flow: We provide one of the first almost linear time algorithms for approximately solving undirected maximum flow improving upon the previous fastest running time by a factor of [mathematical formula] for graphs with n vertices. -- Laplacian System Solvers: We improve upon the previous best known algorithms for solving Laplacian systems in standard unit cost RAM model, achieving a running time of [mathematical formula] for solving a Laplacian system of equations. -- Linear System Solvers: We obtain a faster asymptotic running time than conjugate gradient for solving a broad class of symmetric positive definite systems of equations. * More: We improve the running time for multiple problems including regression, generalized lossy flow, multicommodity flow, and more.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

Author : Josep Diaz
Publisher : Springer
ISBN 13 : 3540380450
Total Pages : 532 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques by : Josep Diaz

Download or read book Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques written by Josep Diaz and published by Springer. This book was released on 2006-08-29 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the joint refereed proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and the 10th International Workshop on Randomization and Computation, RANDOM 2006. The book presents 44 carefully reviewed and revised full papers. Among the topics covered are design and analysis of approximation algorithms, hardness of approximation problems, small spaces and data streaming algorithms, embeddings and metric space methods, and more.

Handbook of Combinatorial Optimization

Author : Ding-Zhu Du
Publisher : Springer Science & Business Media
ISBN 13 : 1461303036
Total Pages : 2410 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Handbook of Combinatorial Optimization by : Ding-Zhu Du

Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 2410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air line crew scheduling, corporate planning, computer-aided design and man ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi tion, linear programming relaxations are often the basis for many approxi mation algorithms for solving NP-hard problems (e.g. dual heuristics).

Iterative Methods for Optimization

Author : C. T. Kelley
Publisher : SIAM
ISBN 13 : 9781611970920
Total Pages : 195 pages
Book Rating : 4.9/5 (79 download)

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Book Synopsis Iterative Methods for Optimization by : C. T. Kelley

Download or read book Iterative Methods for Optimization written by C. T. Kelley and published by SIAM. This book was released on 1999-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods. Each of the main algorithms in the text is described in pseudocode, and a collection of MATLAB codes is available. Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages.

Combinatorial Optimization

Author : Bernhard Korte
Publisher : Springer Science & Business Media
ISBN 13 : 3540292977
Total Pages : 596 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Combinatorial Optimization by : Bernhard Korte

Download or read book Combinatorial Optimization written by Bernhard Korte and published by Springer Science & Business Media. This book was released on 2006-01-27 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Cross-Entropy Method

Author : Reuven Y. Rubinstein
Publisher : Springer Science & Business Media
ISBN 13 : 1475743211
Total Pages : 316 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Cross-Entropy Method by : Reuven Y. Rubinstein

Download or read book The Cross-Entropy Method written by Reuven Y. Rubinstein and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rubinstein is the pioneer of the well-known score function and cross-entropy methods. Accessible to a broad audience of engineers, computer scientists, mathematicians, statisticians and in general anyone, theorist and practitioner, who is interested in smart simulation, fast optimization, learning algorithms, and image processing.

Iterative Computer Algorithms with Applications in Engineering

Author : Sadiq M. Sait
Publisher : Wiley-IEEE Computer Society Press
ISBN 13 :
Total Pages : 418 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Iterative Computer Algorithms with Applications in Engineering by : Sadiq M. Sait

Download or read book Iterative Computer Algorithms with Applications in Engineering written by Sadiq M. Sait and published by Wiley-IEEE Computer Society Press. This book was released on 1999 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book includes an introduction to fuzzy logic and its application in the formulation of multi-objective optimization problems, a discussion on hybrid techniques that combine features of heuristics, a survey of recent research work, and examples that illustrate required mathematical concepts."--BOOK JACKET.

Nonlinear Combinatorial Optimization

Author : Ding-Zhu Du
Publisher : Springer
ISBN 13 : 3030161943
Total Pages : 315 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Nonlinear Combinatorial Optimization by : Ding-Zhu Du

Download or read book Nonlinear Combinatorial Optimization written by Ding-Zhu Du and published by Springer. This book was released on 2019-05-31 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate students and researchers in applied mathematics, optimization, engineering, computer science, and management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization. Nonlinear combinatorial optimization is a new research area within combinatorial optimization and includes numerous applications to technological developments, such as wireless communication, cloud computing, data science, and social networks. Theoretical developments including discrete Newton methods, primal-dual methods with convex relaxation, submodular optimization, discrete DC program, along with several applications are discussed and explored in this book through articles by leading experts.

Computational Combinatorial Optimization

Author : Michael Jünger
Publisher : Springer Science & Business Media
ISBN 13 : 3540428771
Total Pages : 317 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Computational Combinatorial Optimization by : Michael Jünger

Download or read book Computational Combinatorial Optimization written by Michael Jünger and published by Springer Science & Business Media. This book was released on 2001-11-21 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This tutorial contains written versions of seven lectures on Computational Combinatorial Optimization given by leading members of the optimization community. The lectures introduce modern combinatorial optimization techniques, with an emphasis on branch and cut algorithms and Lagrangian relaxation approaches. Polyhedral combinatorics as the mathematical backbone of successful algorithms are covered from many perspectives, in particular, polyhedral projection and lifting techniques and the importance of modeling are extensively discussed. Applications to prominent combinatorial optimization problems, e.g., in production and transport planning, are treated in many places; in particular, the book contains a state-of-the-art account of the most successful techniques for solving the traveling salesman problem to optimality.

Integer and Combinatorial Optimization

Author : Laurence A. Wolsey
Publisher : John Wiley & Sons
ISBN 13 : 1118626869
Total Pages : 782 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Integer and Combinatorial Optimization by : Laurence A. Wolsey

Download or read book Integer and Combinatorial Optimization written by Laurence A. Wolsey and published by John Wiley & Sons. This book was released on 2014-08-28 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION "This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list."-Optima "A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for understanding the structure of and solving the resulting integer programming problems."-Computing Reviews "[This book] can serve as a basis for various graduate courses on discrete optimization as well as a reference book for researchers and practitioners."-Mathematical Reviews "This comprehensive and wide-ranging book will undoubtedly become a standard reference book for all those in the field of combinatorial optimization."-Bulletin of the London Mathematical Society "This text should be required reading for anybody who intends to do research in this area or even just to keep abreast of developments."-Times Higher Education Supplement, London Also of interest . . . INTEGER PROGRAMMING Laurence A. Wolsey Comprehensive and self-contained, this intermediate-level guide to integer programming provides readers with clear, up-to-date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively. 1998 (0-471-28366-5) 260 pp.

Combinatorial And Global Optimization

Author : Rainer E Burkard
Publisher : World Scientific
ISBN 13 : 9814489654
Total Pages : 373 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Combinatorial And Global Optimization by : Rainer E Burkard

Download or read book Combinatorial And Global Optimization written by Rainer E Burkard and published by World Scientific. This book was released on 2002-04-05 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, biological science, and computer science. In combinatorial optimization and graph theory, many approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. Recent major successes based on these approaches include interior point algorithms for linear and discrete problems, the celebrated Goemans-Williamson relaxation of the maximum cut problem, and the Du-Hwang solution of the Gilbert-Pollak conjecture. Since integer constraints are equivalent to nonconvex constraints, the fundamental difference between classes of optimization problems is not between discrete and continuous problems but between convex and nonconvex optimization problems. This volume is a selection of refereed papers based on talks presented at a conference on “Combinatorial and Global Optimization” held at Crete, Greece.

Iterative Optimization in Inverse Problems

Author : Charles Byrne
Publisher : CRC Press
ISBN 13 : 1482222345
Total Pages : 298 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Iterative Optimization in Inverse Problems by : Charles Byrne

Download or read book Iterative Optimization in Inverse Problems written by Charles Byrne and published by CRC Press. This book was released on 2014-02-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author's considerable research in the field, including his recently developed class of SUMMA algorithms

Handbook of combinatorial optimization. 1

Author : Dingzhu Du
Publisher : Springer Science & Business Media
ISBN 13 : 9780792350187
Total Pages : 808 pages
Book Rating : 4.3/5 (51 download)

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Book Synopsis Handbook of combinatorial optimization. 1 by : Dingzhu Du

Download or read book Handbook of combinatorial optimization. 1 written by Dingzhu Du and published by Springer Science & Business Media. This book was released on 1998 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of a multi-volume set, which deals with several algorithmic approaches for discrete problems as well as many combinatorial problems. It is addressed to researchers in discrete optimization, and to all scientists who use combinatorial optimization methods to model and solve problems.

Iterative Methods for Nonlinear Optimization Problems

Author : Samuel L. S. Jacoby
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 294 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Iterative Methods for Nonlinear Optimization Problems by : Samuel L. S. Jacoby

Download or read book Iterative Methods for Nonlinear Optimization Problems written by Samuel L. S. Jacoby and published by Prentice Hall. This book was released on 1972 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

Author : Sanjeev Arora
Publisher : Springer Science & Business Media
ISBN 13 : 3540407707
Total Pages : 418 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques by : Sanjeev Arora

Download or read book Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques written by Sanjeev Arora and published by Springer Science & Business Media. This book was released on 2003-08-13 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 6th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2003 and of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, held in Princeton, NY, USA in August 2003. The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. Among the issues addressed are design and analysis of randomized and approximation algorithms, online algorithms, complexity theory, combinatorial structures, error-correcting codes, pseudorandomness, derandomization, network algorithms, random walks, Markov chains, probabilistic proof systems, computational learning, randomness in cryptography, and various applications.

Introduction to Combinatorial Optimization

Author : Ding-Zhu Du
Publisher : Springer Nature
ISBN 13 : 3031105966
Total Pages : 407 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Introduction to Combinatorial Optimization by : Ding-Zhu Du

Download or read book Introduction to Combinatorial Optimization written by Ding-Zhu Du and published by Springer Nature. This book was released on 2022-09-26 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields. There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems. Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization. Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, such as greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer. Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.