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Author | : J. E. Dennis, Jr. |
Publisher | : SIAM |
Total Pages | : 394 |
Release | : 1996-12-01 |
Genre | : Mathematics |
ISBN | : 9781611971200 |
Download Numerical Methods for Unconstrained Optimization and Nonlinear Equations Book in PDF, ePub and Kindle
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Author | : L.T. Watson |
Publisher | : Elsevier |
Total Pages | : 382 |
Release | : 2001-03-14 |
Genre | : Mathematics |
ISBN | : 0080929540 |
Download Nonlinear Equations and Optimisation Book in PDF, ePub and Kindle
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! In one of the papers in this collection, the remark that "nothing at all takes place in the universe in which some rule of maximum of minimum does not appear" is attributed to no less an authority than Euler. Simplifying the syntax a little, we might paraphrase this as Everything is an optimization problem. While this might be something of an overstatement, the element of exaggeration is certainly reduced if we consider the extended form: Everything is an optimization problem or a system of equations. This observation, even if only partly true, stands as a fitting testimonial to the importance of the work covered by this volume. Since the 1960s, much effort has gone into the development and application of numerical algorithms for solving problems in the two areas of optimization and systems of equations. As a result, many different ideas have been proposed for dealing efficiently with (for example) severe nonlinearities and/or very large numbers of variables. Libraries of powerful software now embody the most successful of these ideas, and one objective of this volume is to assist potential users in choosing appropriate software for the problems they need to solve. More generally, however, these collected review articles are intended to provide both researchers and practitioners with snapshots of the 'state-of-the-art' with regard to algorithms for particular classes of problem. These snapshots are meant to have the virtues of immediacy through the inclusion of very recent ideas, but they also have sufficient depth of field to show how ideas have developed and how today's research questions have grown out of previous solution attempts. The most efficient methods for local optimization, both unconstrained and constrained, are still derived from the classical Newton approach. As well as dealing in depth with the various classical, or neo-classical, approaches, the selection of papers on optimization in this volume ensures that newer ideas are also well represented. Solving nonlinear algebraic systems of equations is closely related to optimization. The two are not completely equivalent, however, and usually something is lost in the translation. Algorithms for nonlinear equations can be roughly classified as locally convergent or globally convergent. The characterization is not perfect. Locally convergent algorithms include Newton's method, modern quasi-Newton variants of Newton's method, and trust region methods. All of these approaches are well represented in this volume.
Author | : Layne T. Watson |
Publisher | : |
Total Pages | : 371 |
Release | : 2000 |
Genre | : |
ISBN | : |
Download Optimization and Nonlinear Equations Book in PDF, ePub and Kindle
Author | : L.T. Watson |
Publisher | : Gulf Professional Publishing |
Total Pages | : 392 |
Release | : 2001-03-28 |
Genre | : Mathematics |
ISBN | : 9780444505996 |
Download Nonlinear Equations and Optimisation Book in PDF, ePub and Kindle
After a review of historical developments in convergence analysis for Newton's and Newton-like methods, 18 papers deal in depth with various classical, or neo-classical approaches, as well as newer ideas on optimization and solving linear equations. A sampling of topics: truncated Newton methods, sequential quadratic programming for large- scale nonlinear optimization, and automatic differentiation of algorithms. This monograph, one of seven volumes in the set, is also published as the Journal of Computational and Applied Mathematics; v.124 (2000). Indexed only by author. c. Book News Inc.
Author | : Andrzej Ruszczynski |
Publisher | : Princeton University Press |
Total Pages | : 463 |
Release | : 2011-09-19 |
Genre | : Mathematics |
ISBN | : 1400841054 |
Download Nonlinear Optimization Book in PDF, ePub and Kindle
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.
Author | : Luigi Grippo |
Publisher | : Springer Nature |
Total Pages | : 721 |
Release | : 2023-05-27 |
Genre | : Mathematics |
ISBN | : 3031267907 |
Download Introduction to Methods for Nonlinear Optimization Book in PDF, ePub and Kindle
This book has two main objectives: • to provide a concise introduction to nonlinear optimization methods, which can be used as a textbook at a graduate or upper undergraduate level; • to collect and organize selected important topics on optimization algorithms, not easily found in textbooks, which can provide material for advanced courses or can serve as a reference text for self-study and research. The basic material on unconstrained and constrained optimization is organized into two blocks of chapters: • basic theory and optimality conditions • unconstrained and constrained algorithms. These topics are treated in short chapters that contain the most important results in theory and algorithms, in a way that, in the authors’ experience, is suitable for introductory courses. A third block of chapters addresses methods that are of increasing interest for solving difficult optimization problems. Difficulty can be typically due to the high nonlinearity of the objective function, ill-conditioning of the Hessian matrix, lack of information on first-order derivatives, the need to solve large-scale problems. In the book various key subjects are addressed, including: exact penalty functions and exact augmented Lagrangian functions, non monotone methods, decomposition algorithms, derivative free methods for nonlinear equations and optimization problems. The appendices at the end of the book offer a review of the essential mathematical background, including an introduction to convex analysis that can make part of an introductory course.
Author | : Francisco J. Aragón |
Publisher | : Springer |
Total Pages | : 350 |
Release | : 2019-02-27 |
Genre | : Mathematics |
ISBN | : 3030111849 |
Download Nonlinear Optimization Book in PDF, ePub and Kindle
This textbook on nonlinear optimization focuses on model building, real world problems, and applications of optimization models to natural and social sciences. Organized into two parts, this book may be used as a primary text for courses on convex optimization and non-convex optimization. Definitions, proofs, and numerical methods are well illustrated and all chapters contain compelling exercises. The exercises emphasize fundamental theoretical results on optimality and duality theorems, numerical methods with or without constraints, and derivative-free optimization. Selected solutions are given. Applications to theoretical results and numerical methods are highlighted to help students comprehend methods and techniques.
Author | : Igor Griva |
Publisher | : SIAM |
Total Pages | : 743 |
Release | : 2009-01-01 |
Genre | : Mathematics |
ISBN | : 0898717736 |
Download Linear and Nonlinear Optimization Book in PDF, ePub and Kindle
Provides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication.
Author | : Eligius M.T. Hendrix |
Publisher | : Springer |
Total Pages | : 218 |
Release | : 2010-04-27 |
Genre | : Mathematics |
ISBN | : 0387886702 |
Download Introduction to Nonlinear and Global Optimization Book in PDF, ePub and Kindle
This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization which includes the presentation of numerous algorithms, examples, and illustrations, designed to improve the reader’s intuition and develop the analytical skills needed to identify optimization problems, classify the structure of a model, and determine whether a solution fulfills optimality conditions.
Author | : Neculai Andrei |
Publisher | : Springer Science & Business Media |
Total Pages | : 356 |
Release | : 2013-06-22 |
Genre | : Mathematics |
ISBN | : 1461467977 |
Download Nonlinear Optimization Applications Using the GAMS Technology Book in PDF, ePub and Kindle
Here is a collection of nonlinear optimization applications from the real world, expressed in the General Algebraic Modeling System (GAMS). The concepts are presented so that the reader can quickly modify and update them to represent real-world situations.