Numerical methods for unconstrained optimization and nonlinear equations
 Author/Creator
 Dennis, J. E. (John E.), 1939
 Language
 English.
 Imprint
 Philadelphia : Society for Industrial and Applied Mathematics, c1996.
 Physical description
 xv, 378 p. : ill. ; 23 cm.
 Series
 Classics in applied mathematics ; 16.
Access
Available online

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QA402.5 .D44 1996

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QA402.5 .D44 1996
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Contributors
 Contributor
 Schnabel, Robert B.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 364370) and indexes.
 Contents

 Preface 1. Introduction. Problems to be considered Characteristics of 'realworld' problems Finiteprecision arithmetic and measurement of error Exercises 2. Nonlinear Problems in One Variable. What is not possible Newton's method for solving one equation in one unknown Convergence of sequences of real numbers Convergence of Newton's method Globally convergent methods for solving one equation in one uknown Methods when derivatives are unavailable Minimization of a function of one variable Exercises 3. Numerical Linear Algebra Background. Vector and matrix norms and orthogonality Solving systems of linear equationsmatrix factorizations Errors in solving linear systems Updating matrix factorizations Eigenvalues and positive definiteness Linear least squares Exercises 4. Multivariable Calculus Background Derivatives and multivariable models Multivariable finitedifference derivatives Necessary and sufficient conditions for unconstrained minimization Exercises 5. Newton's Method for Nonlinear Equations and Unconstrained Minimization. Newton's method for systems of nonlinear equations Local convergence of Newton's method The Kantorovich and contractive mapping theorems Finitedifference derivative methods for systems of nonlinear equations Newton's method for unconstrained minimization Finite difference derivative methods for unconstrained minimization Exercises 6. Globally Convergent Modifications of Newton's Method. The quasiNewton framework Descent directions Line searches The modeltrust region approach Global methods for systems of nonlinear equations Exercises 7. Stopping, Scaling, and Testing. Scaling Stopping criteria Testing Exercises 8. Secant Methods for Systems of Nonlinear Equations. Broyden's method Local convergence analysis of Broyden's method Implementation of quasiNewton algorithms using Broyden's update Other secant updates for nonlinear equations Exercises 9. Secant Methods for Unconstrained Minimization. The symmetric secant update of Powell Symmetric positive definite secant updates Local convergence of positive definite secant methods Implementation of quasiNewton algorithms using the positive definite secant update Another convergence result for the positive definite secant method Other secant updates for unconstrained minimization Exercises 10. Nonlinear Least Squares. The nonlinear leastsquares problem GaussNewtontype methods Full Newtontype methods Other considerations in solving nonlinear leastsquares problems Exercises 11. Methods for Problems with Special Structure. The sparse finitedifference Newton method Sparse secant methods Deriving leastchange secant updates Analyzing leastchange secant methods Exercises Appendix A. A Modular System of Algorithms for Unconstrained Minimization and Nonlinear Equations (by Robert Schnabel) Appendix B. Test Problems (by Robert Schnabel) References Author Index Subject Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This book has become the standard for a complete, stateoftheart 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 'quasiNewton' 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.
(source: Nielsen Book Data)  Supplemental links

Table of contents
Publisher description
Subjects
 Subject
 Mathematical optimization.
 Equations > Numerical solutions.
 minimisation.
 méthode Newton.
 méthode numérique.
 optimisation sans contrainte.
 système équation non linéaire.
 optimisation mathématique.
 Programação matemática.
 Métodos numéricos de otimização.
 Équations > Solutions numériques.
 Équations > Solutions numériques > Problèmes et exercices.
 Optimisation mathématique.
 Optimisation mathématique > Problèmes et exercices.
 Analyse numérique.
 Gene Golub Library.
Bibliographic information
 Reprint/reissue date
 1996
 Original date
 1983
 Responsibility
 J.E. Dennis, Jr., Robert B. Schnabel.
 Series
 Classics in applied mathematics ; 16
 Note
 Originally published: Englewood Cliffs, N.J. : PrenticeHall, c1983.
 ISBN
 0898713641 (pbk.)
 9780898713640 (pbk.)