Approximation And Complexity In Numerical Optimization

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Approximation and Complexity in Numerical Optimization

Author : Panos M. Pardalos
Publisher : Springer Science & Business Media
ISBN 13 : 1475731450
Total Pages : 597 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Approximation and Complexity in Numerical Optimization by : Panos M. Pardalos

Download or read book Approximation and Complexity in Numerical Optimization written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complexity in Numerical Optimization

Author : Panos M. Pardalos
Publisher : World Scientific
ISBN 13 : 9789810214159
Total Pages : 536 pages
Book Rating : 4.2/5 (141 download)

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Book Synopsis Complexity in Numerical Optimization by : Panos M. Pardalos

Download or read book Complexity in Numerical Optimization written by Panos M. Pardalos and published by World Scientific. This book was released on 1993 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Approximation and Optimization

Author : Ioannis C. Demetriou
Publisher : Springer
ISBN 13 : 3030127672
Total Pages : 237 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Approximation and Optimization by : Ioannis C. Demetriou

Download or read book Approximation and Optimization written by Ioannis C. Demetriou and published by Springer. This book was released on 2019-05-10 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimization. Chapters discuss state of the art topics with highly relevant applications throughout science, engineering, technology and social sciences. Academics, researchers, data science practitioners, business analysts, social sciences investigators and graduate students will find the number of illustrations, applications, and examples provided useful. This volume is based on the conference Approximation and Optimization: Algorithms, Complexity, and Applications, which was held in the National and Kapodistrian University of Athens, Greece, June 29–30, 2017. The mix of survey and research content includes topics in approximations to discrete noisy data; binary sequences; design of networks and energy systems; fuzzy control; large scale optimization; noisy data; data-dependent approximation; networked control systems; machine learning ; optimal design; no free lunch theorem; non-linearly constrained optimization; spectroscopy.

Complexity and Approximation

Author : Giorgio Ausiello
Publisher : Springer Science & Business Media
ISBN 13 : 3642584128
Total Pages : 536 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Complexity and Approximation by : Giorgio Ausiello

Download or read book Complexity and Approximation written by Giorgio Ausiello and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Approximation Algorithms for Combinatorial Optimization

Author : Klaus Jansen
Publisher : Springer
ISBN 13 : 354044436X
Total Pages : 282 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Approximation Algorithms for Combinatorial Optimization by : Klaus Jansen

Download or read book Approximation Algorithms for Combinatorial Optimization written by Klaus Jansen and published by Springer. This book was released on 2003-07-31 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2000, held in Saarbrcken, Germany in September 2000. The 22 revised full papers presented together with four invited contributions were carefully reviewed and selected from 68 submissions. The topics dealt with include design and analysis of approximation algorithms, inapproximibility results, on-line problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and various applications.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

Author : Anupam Gupta
Publisher : Springer
ISBN 13 : 3642325122
Total Pages : 687 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques by : Anupam Gupta

Download or read book Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques written by Anupam Gupta and published by Springer. This book was released on 2012-07-20 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012, and the 16th International Workshop on Randomization and Computation, RANDOM 2012, held in Cambridge, Massachusetts, USA, in August 2011. The volume contains 28 contributed papers, selected by the APPROX Program Committee out of 70 submissions, and 28 contributed papers, selected by the RANDOM Program Committee out of 67 submissions. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.

Handbook of Approximation Algorithms and Metaheuristics

Author : Teofilo F. Gonzalez
Publisher : CRC Press
ISBN 13 : 1420010743
Total Pages : 1434 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Approximation Algorithms and Metaheuristics by : Teofilo F. Gonzalez

Download or read book Handbook of Approximation Algorithms and Metaheuristics written by Teofilo F. Gonzalez and published by CRC Press. This book was released on 2007-05-15 with total page 1434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical applications. It is the first book to comprehensively study both approximation algorithms and metaheuristics. Starting with basic approaches, the handbook presents the methodologies to design and analyze efficient approximation algorithms for a large class of problems, and to establish inapproximability results for another class of problems. It also discusses local search, neural networks, and metaheuristics, as well as multiobjective problems, sensitivity analysis, and stability. After laying this foundation, the book applies the methodologies to classical problems in combinatorial optimization, computational geometry, and graph problems. In addition, it explores large-scale and emerging applications in networks, bioinformatics, VLSI, game theory, and data analysis. Undoubtedly sparking further developments in the field, this handbook provides the essential techniques to apply approximation algorithms and metaheuristics to a wide range of problems in computer science, operations research, computer engineering, and economics. Armed with this information, researchers can design and analyze efficient algorithms to generate near-optimal solutions for a wide range of computational intractable problems.

Approximation Algorithms and Semidefinite Programming

Author : Bernd Gärtner
Publisher : Springer Science & Business Media
ISBN 13 : 3642220150
Total Pages : 253 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Approximation Algorithms and Semidefinite Programming by : Bernd Gärtner

Download or read book Approximation Algorithms and Semidefinite Programming written by Bernd Gärtner and published by Springer Science & Business Media. This book was released on 2012-01-10 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms, computational complexity, graph theory, geometry, real algebraic geometry and quantum computing. This book is an introduction to selected aspects of semidefinite programming and its use in approximation algorithms. It covers the basics but also a significant amount of recent and more advanced material. There are many computational problems, such as MAXCUT, for which one cannot reasonably expect to obtain an exact solution efficiently, and in such case, one has to settle for approximate solutions. For MAXCUT and its relatives, exciting recent results suggest that semidefinite programming is probably the ultimate tool. Indeed, assuming the Unique Games Conjecture, a plausible but as yet unproven hypothesis, it was shown that for these problems, known algorithms based on semidefinite programming deliver the best possible approximation ratios among all polynomial-time algorithms. This book follows the “semidefinite side” of these developments, presenting some of the main ideas behind approximation algorithms based on semidefinite programming. It develops the basic theory of semidefinite programming, presents one of the known efficient algorithms in detail, and describes the principles of some others. It also includes applications, focusing on approximation algorithms.

Approximation Algorithms for Combinatorial Optimization

Author : Klaus Jansen
Publisher :
ISBN 13 : 9783662188859
Total Pages : 292 pages
Book Rating : 4.1/5 (888 download)

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Book Synopsis Approximation Algorithms for Combinatorial Optimization by : Klaus Jansen

Download or read book Approximation Algorithms for Combinatorial Optimization written by Klaus Jansen and published by . This book was released on 2014-01-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in Optimization and Approximation

Author : Ding-Zhu Du
Publisher : Springer Science & Business Media
ISBN 13 : 1461336295
Total Pages : 402 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Advances in Optimization and Approximation by : Ding-Zhu Du

Download or read book Advances in Optimization and Approximation written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of research papers in optimization and approximation dedicated to Professor Minyi Yue of the Institute of Applied Mathematics, Beijing, China. The papers provide a broad spectrum of research on optimization problems, including scheduling, location, assignment, linear and nonlinear programming problems as well as problems in molecular biology. The emphasis of the book is on algorithmic aspects of research work in optimization. Special attention is paid to approximation algorithms, including heuristics for combinatorial approximation problems, approximation algorithms for global optimization problems, and applications of approximations in real problems. The work provides the state of the art for researchers in mathematical programming, operations research, theoretical computer science and applied mathematics.

Handbook of Approximation Algorithms and Metaheuristics

Author : Teofilo F. Gonzalez
Publisher : CRC Press
ISBN 13 : 1351235419
Total Pages : 780 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Handbook of Approximation Algorithms and Metaheuristics by : Teofilo F. Gonzalez

Download or read book Handbook of Approximation Algorithms and Metaheuristics written by Teofilo F. Gonzalez and published by CRC Press. This book was released on 2018-05-15 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Approximation Algorithms and Metaheuristics, Second Edition reflects the tremendous growth in the field, over the past two decades. Through contributions from leading experts, this handbook provides a comprehensive introduction to the underlying theory and methodologies, as well as the various applications of approximation algorithms and metaheuristics. Volume 1 of this two-volume set deals primarily with methodologies and traditional applications. It includes restriction, relaxation, local ratio, approximation schemes, randomization, tabu search, evolutionary computation, local search, neural networks, and other metaheuristics. It also explores multi-objective optimization, reoptimization, sensitivity analysis, and stability. Traditional applications covered include: bin packing, multi-dimensional packing, Steiner trees, traveling salesperson, scheduling, and related problems. Volume 2 focuses on the contemporary and emerging applications of methodologies to problems in combinatorial optimization, computational geometry and graphs problems, as well as in large-scale and emerging application areas. It includes approximation algorithms and heuristics for clustering, networks (sensor and wireless), communication, bioinformatics search, streams, virtual communities, and more. About the Editor Teofilo F. Gonzalez is a professor emeritus of computer science at the University of California, Santa Barbara. He completed his Ph.D. in 1975 from the University of Minnesota. He taught at the University of Oklahoma, the Pennsylvania State University, and the University of Texas at Dallas, before joining the UCSB computer science faculty in 1984. He spent sabbatical leaves at the Monterrey Institute of Technology and Higher Education and Utrecht University. He is known for his highly cited pioneering research in the hardness of approximation; for his sublinear and best possible approximation algorithm for k-tMM clustering; for introducing the open-shop scheduling problem as well as algorithms for its solution that have found applications in numerous research areas; as well as for his research on problems in the areas of job scheduling, graph algorithms, computational geometry, message communication, wire routing, etc.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

Author : Josep Diaz
Publisher : Springer Science & Business Media
ISBN 13 : 3540380442
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 Science & Business Media. This book was released on 2006-08-11 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.

Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques

Author : Ashish Goel
Publisher : Springer Science & Business Media
ISBN 13 : 3540853626
Total Pages : 614 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques by : Ashish Goel

Download or read book Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques written by Ashish Goel and published by Springer Science & Business Media. This book was released on 2008-08-12 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and the 12th International Workshop on Randomization and Computation, RANDOM 2008, held in Boston, MA, USA, in August 2008. The 20 revised full papers of the APPROX 2008 workshop were carefully reviewed and selected from 42 submissions and focus on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM 2008 is concerned with applications of randomness to computational and combinatorial problems and accounts for 27 revised full papers, also diligently reviewed and selected out of 52 workshop submissions.

Evaluation Complexity of Algorithms for Nonconvex Optimization

Author : Coralia Cartis
Publisher : SIAM
ISBN 13 : 1611976995
Total Pages : 549 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Evaluation Complexity of Algorithms for Nonconvex Optimization by : Coralia Cartis

Download or read book Evaluation Complexity of Algorithms for Nonconvex Optimization written by Coralia Cartis and published by SIAM. This book was released on 2022-07-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: A popular way to assess the “effort” needed to solve a problem is to count how many evaluations of the problem functions (and their derivatives) are required. In many cases, this is often the dominating computational cost. Given an optimization problem satisfying reasonable assumptions—and given access to problem-function values and derivatives of various degrees—how many evaluations might be required to approximately solve the problem? Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives addresses this question for nonconvex optimization problems, those that may have local minimizers and appear most often in practice. This is the first book on complexity to cover topics such as composite and constrained optimization, derivative-free optimization, subproblem solution, and optimal (lower and sharpness) bounds for nonconvex problems. It is also the first to address the disadvantages of traditional optimality measures and propose useful surrogates leading to algorithms that compute approximate high-order critical points, and to compare traditional and new methods, highlighting the advantages of the latter from a complexity point of view. This is the go-to book for those interested in solving nonconvex optimization problems. It is suitable for advanced undergraduate and graduate students in courses on advanced numerical analysis, data science, numerical optimization, and approximation theory.

Approximation Algorithms

Author : Vijay V. Vazirani
Publisher : Springer
ISBN 13 : 9783662045664
Total Pages : 380 pages
Book Rating : 4.0/5 (456 download)

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Book Synopsis Approximation Algorithms by : Vijay V. Vazirani

Download or read book Approximation Algorithms written by Vijay V. Vazirani and published by Springer. This book was released on 2013-01-18 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians.

Approximation Algorithms for Combinatorial Optimization

Author : Klaus Jansen
Publisher : Springer
ISBN 13 : 9783540679967
Total Pages : 0 pages
Book Rating : 4.6/5 (799 download)

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Book Synopsis Approximation Algorithms for Combinatorial Optimization by : Klaus Jansen

Download or read book Approximation Algorithms for Combinatorial Optimization written by Klaus Jansen and published by Springer. This book was released on 2000-08-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2000, held in Saarbrücken, Germany in September 2000. The 22 revised full papers presented together with four invited contributions were carefully reviewed and selected from 68 submissions. The topics dealt with include design and analysis of approximation algorithms, inapproximibility results, on-line problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and various applications.