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Author: M. F. MacGuire
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Author: M. F. MacGuire
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Author: M. J. D. Powell
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 24
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Author: Neculai Andrei
Publisher: Springer Nature
ISBN: 3030429504
Category : Mathematics
Languages : en
Pages : 515
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Book Description
Two approaches are known for solving large-scale unconstrained optimization problems—the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.
Author: Donald O. Thompson
Publisher: Springer Science & Business Media
ISBN: 9780306447310
Category : Technology & Engineering
Languages : en
Pages : 1188
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Proceedings of the Thirteenth Symposium on Quantitative Nondestructive Evaluation held in Brunswick, Maine, August 1-6, 1993
Author: Donghun Suh
Publisher:
ISBN:
Category : Conjugate gradient methods
Languages : en
Pages : 176
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Author: Dan Gabriel Cacuci
Publisher: CRC Press
ISBN: 1584887354
Category : Mathematics
Languages : en
Pages : 376
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Book Description
Data evaluation and data combination require the use of a wide range of probability theory concepts and tools, from deductive statistics mainly concerning frequencies and sample tallies to inductive inference for assimilating non-frequency data and a priori knowledge. Computational Methods for Data Evaluation and Assimilation presents interdisciplinary methods for integrating experimental and computational information. This self-contained book shows how the methods can be applied in many scientific and engineering areas. After presenting the fundamentals underlying the evaluation of experimental data, the book explains how to estimate covariances and confidence intervals from experimental data. It then describes algorithms for both unconstrained and constrained minimization of large-scale systems, such as time-dependent variational data assimilation in weather prediction and similar applications in the geophysical sciences. The book also discusses several basic principles of four-dimensional variational assimilation (4D VAR) and highlights specific difficulties in applying 4D VAR to large-scale operational numerical weather prediction models.
Author: David G. Luenberger
Publisher: Springer
ISBN: 3319188429
Category : Business & Economics
Languages : en
Pages : 547
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Book Description
This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve a problem. This was a major theme of the first edition of this book and the fourth edition expands and further illustrates this relationship. As in the earlier editions, the material in this fourth edition is organized into three separate parts. Part I is a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. It is possible to go directly into Parts II and III omitting Part I, and, in fact, the book has been used in this way in many universities. New to this edition is a chapter devoted to Conic Linear Programming, a powerful generalization of Linear Programming. Indeed, many conic structures are possible and useful in a variety of applications. It must be recognized, however, that conic linear programming is an advanced topic, requiring special study. Another important topic is an accelerated steepest descent method that exhibits superior convergence properties, and for this reason, has become quite popular. The proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8. As in previous editions, end-of-chapter exercises appear for all chapters. From the reviews of the Third Edition: “... this very well-written book is a classic textbook in Optimization. It should be present in the bookcase of each student, researcher, and specialist from the host of disciplines from which practical optimization applications are drawn.” (Jean-Jacques Strodiot, Zentralblatt MATH, Vol. 1207, 2011)
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 288
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Author: Bruno Carpentieri
Publisher: BoD – Books on Demand
ISBN: 1789239052
Category : Mathematics
Languages : en
Pages : 160
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Book Description
This book contains well-written monographs within the broad spectrum of applied mathematics, offering an interesting reading of some of the current trends and problems in this fascinating and critically important field of science to a broad category of researchers and practitioners. Recent developments in high-performance computing are radically changing the way we do numerics. As the size of problems is expected to grow very large in the future, the gap between fast and slow algorithms is growing rapidly. Novel classes of numerical methods with reduced computational complexity are therefore needed to make the rigorous numerical solution of difficult problems arising in an industrial setting more affordable. The book is structured in four distinct parts, according to the purpose and approaches used in the development of the contributions, ranging from optimization techniques to graph-oriented approaches and approximation theory, providing a good mix of both theory and practice.
Author: Kenneth H. Brink
Publisher: Harvard University Press
ISBN: 9780674017405
Category : Political Science
Languages : en
Pages : 630
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