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Nonlinear Equations And Optimisation

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Numerical Methods For Unconstrained Optimization And Nonlinear Equations

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Author : J. E. Dennis, Jr.
language : en
Publisher: SIAM
Release Date : 1996-12-01

Numerical Methods For Unconstrained Optimization And Nonlinear Equations written by J. E. Dennis, Jr. and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-01 with Mathematics categories.

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.

Nonlinear Equations And Optimisation

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Author : L.T. Watson
language : en
Publisher: Elsevier
Release Date : 2001-03-14

Nonlinear Equations And Optimisation written by L.T. Watson and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-14 with Mathematics categories.

/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.

Nonlinear Optimization

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Author : Francisco J. Aragón
language : en
Publisher: Springer
Release Date : 2019-02-27

Nonlinear Optimization written by Francisco J. Aragón and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.

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.

Introduction To Nonlinear And Global Optimization

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Author : Eligius M.T. Hendrix
language : en
Publisher: Springer
Release Date : 2010-04-27

Introduction To Nonlinear And Global Optimization written by Eligius M.T. Hendrix and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-27 with Mathematics categories.

Nonlinear Optimization is an intriguing area of study where mathematical theory, algorithms and applications converge to calculate the optimal values of continuous functions. Within this subject, Global Optimization aims at finding global optima for difficult problems in which many local optima might exist. This book provides a compelling introduction to global and non-linear optimization providing interdisciplinary readers with a strong background to continue their studies into these and other related fields. The book offers insight in relevant concepts such as "region of attraction" and "Branch-and-Bound" by elaborating small numerical examples and exercises for the reader to follow.

Linear And Nonlinear Optimization

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Author : Richard W. Cottle
language : en
Publisher: Springer
Release Date : 2017-06-11

Linear And Nonlinear Optimization written by Richard W. Cottle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-11 with Business & Economics categories.

This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia

Nonlinear Optimization

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Author : Andrzej Ruszczynski
language : en
Publisher: Princeton University Press
Release Date : 2011-09-19

Nonlinear Optimization written by Andrzej Ruszczynski and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-19 with Mathematics categories.

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.

Numerical Methods For Unconstrained Optimization And Nonlinear Equations

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Author : J. E. Dennis, Jr.
language : en
Publisher: SIAM
Release Date : 1996-12-01

A complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations.

Nonlinear Equations And Optimisation

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Author : L.T. Watson
language : en
Publisher: Gulf Professional Publishing
Release Date : 2001-03-28

Nonlinear Equations And Optimisation written by L.T. Watson and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-28 with Mathematics categories.

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.

Optimization And Nonlinear Equations

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Author : Layne T. Watson
language : en
Publisher:
Release Date : 2000

Optimization And Nonlinear Equations written by Layne T. Watson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.

Introduction To The Theory Of Nonlinear Optimization

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Author : Johannes Jahn
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-09-17

Introduction To The Theory Of Nonlinear Optimization written by Johannes Jahn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-17 with Mathematics categories.

This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

Nonlinear Equations And Optimisation

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