Computational Complexity of Discrete Optimization Problems PDF Download
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Author: J. K. Lenstra
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
Author: J. K. Lenstra
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
Author: Jan K. Lenstra
Publisher:
ISBN:
Category :
Languages : nl
Pages : 22
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Book Description
Author: R. Gary Parker
Publisher: Elsevier
ISBN: 1483294803
Category : Mathematics
Languages : en
Pages : 485
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Book Description
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas of linear programming, graph theory, and combinatorics--prerequisites for readers of the text. Numerous exercises are included at the end of each chapter.
Author: Giorgio Ausiello
Publisher: Springer Science & Business Media
ISBN: 9783540654315
Category : Business & Economics
Languages : en
Pages : 554
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Book Description
This book documents the state of the art in combinatorial optimization, presenting approximate solutions of virtually all relevant classes of NP-hard optimization problems. The wealth of problems, algorithms, results, and techniques make it an indispensible source of reference for professionals. The text smoothly integrates numerous illustrations, examples, and exercises.
Author: Panos M Pardalos
Publisher: World Scientific
ISBN: 9814504084
Category : Mathematics
Languages : en
Pages : 538
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Book Description
Computational complexity, originated from the interactions between computer science and numerical optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty.The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable.The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions.This book is a collection of articles on recent complexity developments in numerical optimization. The topics covered include complexity of approximation algorithms, new polynomial time algorithms for convex quadratic minimization, interior point algorithms, complexity issues regarding test generation of NP-hard problems, complexity of scheduling problems, min-max, fractional combinatorial optimization, fixed point computations and network flow problems.The collection of articles provide a broad spectrum of the direction in which research is going and help to elucidate the nature of computational complexity in optimization. The book will be a valuable source of information to faculty, students and researchers in numerical optimization and related areas.
Author: Panos M. Pardalos
Publisher: World Scientific
ISBN: 9789810214159
Category : Mathematics
Languages : en
Pages : 536
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Book Description
Computational complexity, originated from the interactions between computer science and numerical optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty.The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable.The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions.This book is a collection of articles on recent complexity developments in numerical optimization. The topics covered include complexity of approximation algorithms, new polynomial time algorithms for convex quadratic minimization, interior point algorithms, complexity issues regarding test generation of NP-hard problems, complexity of scheduling problems, min-max, fractional combinatorial optimization, fixed point computations and network flow problems.The collection of articles provide a broad spectrum of the direction in which research is going and help to elucidate the nature of computational complexity in optimization. The book will be a valuable source of information to faculty, students and researchers in numerical optimization and related areas.
Author: Panos M. Pardalos
Publisher: Springer Science & Business Media
ISBN: 1475731450
Category : Technology & Engineering
Languages : en
Pages : 597
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Book Description
There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed recently that link the discrete universe to the continuous universe through geomet ric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new ap proximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization prob lems, new approximate algorithms have been developed based on semidefinite pro gramming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numeri cal optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty. The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable. The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions. A conference on Approximation and Complexity in Numerical Optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, 1999 at the Center for Applied Optimization of the University of Florida.
Author: E. Boros
Publisher: Elsevier
ISBN: 008093028X
Category : Mathematics
Languages : en
Pages : 587
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Book Description
One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world.This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc.Key features:• state of the art surveys• comprehensiveness• prominent authors• theoretical, computational and applied aspects.This book is a reprint of Discrete Applied Mathematics Volume 23, Numbers 1-3
Author: Benjamin Doerr
Publisher: Springer Nature
ISBN: 3030294145
Category : Computers
Languages : en
Pages : 506
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Book Description
This edited book reports on recent developments in the theory of evolutionary computation, or more generally the domain of randomized search heuristics. It starts with two chapters on mathematical methods that are often used in the analysis of randomized search heuristics, followed by three chapters on how to measure the complexity of a search heuristic: black-box complexity, a counterpart of classical complexity theory in black-box optimization; parameterized complexity, aimed at a more fine-grained view of the difficulty of problems; and the fixed-budget perspective, which answers the question of how good a solution will be after investing a certain computational budget. The book then describes theoretical results on three important questions in evolutionary computation: how to profit from changing the parameters during the run of an algorithm; how evolutionary algorithms cope with dynamically changing or stochastic environments; and how population diversity influences performance. Finally, the book looks at three algorithm classes that have only recently become the focus of theoretical work: estimation-of-distribution algorithms; artificial immune systems; and genetic programming. Throughout the book the contributing authors try to develop an understanding for how these methods work, and why they are so successful in many applications. The book will be useful for students and researchers in theoretical computer science and evolutionary computing.
Author: Panos M. Pardalos
Publisher: American Mathematical Soc.
ISBN: 0821832484
Category : Mathematics
Languages : en
Pages : 194
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Book Description
During the last decade, many novel approaches have been considered for dealing with computationally difficult discrete optimization problems. Such approaches include interior point methods, semidefinite programming techniques, and global optimization. More efficient computational algorithms have been developed and larger problem instances of hard discrete problems have been solved. This progress is due in part to these novel approaches, but also to new computing facilities and massive parallelism. This volume contains the papers presented at the workshop on ``Novel Approaches to Hard Discrete Optimization''. The articles cover a spectrum of issues regarding computationally hard discrete problems.
