国外数学名著系列（续一）（影印版）42：无约束最优化与非线性方程的数值方法

图书标准信息

• 作者 [美]丹尼斯（Dennis J.E.） 著
• 出版社 科学出版社
• 出版时间 2009-01
• 版次 1
• ISBN 9787030234827
• 定价 86.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 378页
• 字数 476千字
• 正文语种 英语
• 丛书 国外数学名著系列:42

【内容简介】

　　《国外数学名著系列(续1)(影印版)42：无约束最优化与非线性方程的数值方法》isastandardforacompletedescriptionofthemethodsforunconstrainedoptimizationandthesolutionofnonlinearequations....thisrepublicationismostwelcomeandthisvolumeshouldbeineverylibrary.Ofcourse，thereexistmorerecentbooksonthetopicsandsomebodyinterestedinthesubjectcannotbesatiatedbylookingonlyatthisbook.However，itcontainsmuchquite-well-presentedmaterialandIrecommendreadingitbeforegoing，toother.publications.

【目录】

PREFACETOTHECLASSICSEDITION
PREFACE
1INTRODUCTION
1.1Problemstobeconsidered
1.2Characteristicsof"real-world"problems
1.3Finite-precisionarithmeticandmeasurementoferror
1.4Exercises
2NONLINEARPROBLEMSINONEVARIABLE
2.1Whatisnotpossible
2.2Newtonsmethodforsolvingoneequationinoneunknown
2.3Convergenceofsequencesofrealnumbers
2.4ConvergenceofNewtonsmethod
2.5Globallyconvergentmethodsforsolvingoneequationinoneunknown
2.6Methodswhenderivativesareunavailable
2.7Minimizationofafunctionofonevariable
2.8Exercises
3NUMERICALLINEARALGEBRABACKGROUND
3.1Vectorandmatrixnormsandorthogonality
3.2Solvingsystemsoflinearequations--matrixfactorizations
3.3Errorsinsolvinglinearsystems
3.4Updatingmatrixfactorizations
3.5Eigenvaluesandpositivedefiniteness
3.6Linearleastsquares
3.7Exercises
4MULTIVARIABLECALCULUSBACKGROUND
4.1Derivativesandmultivariablemodels
4.2Multivariablefinite-differencederivatives
4.3Necessaryandsufficientconditionsforunconstrainedminimization
4.4Exercises83
5NEWTONSMETHODFORNONLINEAREQUATIONSANDUNCONSTRAINEDMINIMIZATION
5.1Newtonsmethodforsystemsofnonlinearequations
5.2LocalconvergenceofNewtonsmethod
5.3TheKantorovichandcontractivemappingtheorems
5.4Finite-differencederivativemethodsforsystemsofnonlinearequations
5.5Newtonsmethodforunconstrainedminimization
5.6Finite-differencederivativemethodsforunconstrainedminimization
5.7Exercises
6GLOBALLYCONVERGENTMODIFICATIONSOFNEWTONSMETHOD
6.1Thequasi-Newtonframework
6.2Descentdirections
6.3Linesearches
6.3.1Convergenceresultsforproperlychosensteps
6.3.2Stepselectionbybacktracking
6.4Themodel-trustregionapproach
6.4.1Thelocallyconstrainedoptimal("hook")step
6.4.2Thedoubledoglegstep
6.4.3Updatingthetrustregion
6.5Globalmethodsforsystemsofnonlinearequations
6.6Exercises
7STOPPING,SCALING,ANDTESTING
7.1Scaling
7.2Stoppingcriteria
7.3Testing
7.4Exercises
8SECANTMETHODSFORSYSTEMSOFNONLINEAREQUATIONS
8.1Broydensmethod
8.2LocalconvergenceanalysisofBroydensmethod
8.3Implementationofquasi-NewtonalgorithmsusingBroydensupdate
8.4Othersecantupdatesfornonlinearequations
8.5Exercises
9SECANTMETHODSFORUNCONSTRAINEDMINIMIZATION
9.1ThesymmetricsecantupdateofPowell
9.2Symmetricpositivedefinitesecantupdates
9.3Localconvergenceofpositivedefinitesecantmethods
9.4Implementationofquasi-Newtonalgorithmsusingthepositivedefinitesecantupdate
9.5Anotherconvergenceresultforthepositivedefinitesecantmethod
9.6Othersecantupdatesforunconstrainedminimization
9.7Exercises
10NONLINEARLEASTSQUARES
10.1Thenonlinearleast-squaresproblem
10.2Gauss-Newton-typemethods
10.3FullNewton-typemethods
10.4Otherconsiderationsinsolvingnonlinearleast-squaresproblems
10.5Exercises
11METHODSFORPROBLEMSWITHSPECIALSTRUCTURE
11.1Thesparsefinite-differenceNewtonmethod
11.2Sparsesecantmethods
11.3Derivingleast-changesecantupdates
11.4Analyzingleast-changesecantmethods
11.5Exercises
AAPPENDIX:AMODULARSYSTEMOFALGORITHMSFORUNCONSTRAINEDMINIMIZATIONANDNONLINEAREQUATIONS(byRobertSchnabel)
BAPPENDIX:TESTPROBLEMS(byRobertSchnabeI)
REFERENCES
AUTHORINDEX
SUBJECTINDEX