隐函数和解映射（英文版）

图书标准信息

• 作者 [美]邓契夫（Dontchev A.L.） 著
• 出版社 世界图书出版公司
• 出版时间 2013-03
• 版次 1
• ISBN 9787510058073
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 373页
• 正文语种 英语

【内容简介】

　　Settingupequationsandsolvingthemhaslongbeensoimportantthat，inpopularimagination，ithasvirtuallycometodescribewhatmathematicalanalysisanditsapplicationsareallabout.Acentralissueinthesubjectiswhetherthesolutiontoanequationinvolvingparametersmaybeviewedasafunctionofthoseparameters，andifso，whatpropertiesthatfunctionmighthave.Thisisaddressedbytheclassicaltheoryofimplicitfunctions，whichbeganwithsinglerealvariablesandprogressedthroughmultiplevariablestoequationsininfinitedimensions，suchasequationsassociatedwithinLegralanddifferentialoperators.

【目录】

Preface
Acknowledgements

Chapter1.Functionsdefinedimplicitlybyequations
1A.Theclassicalinversefunctiontheorem
1B.Theclassicalimplicitfunctiontheorem
1C.Calmness
1D.Lipschitzcontinuity
1E.Lipschitzinvertibilityfromapproximations
1F.Selectionsofmulti-valuedinverses
1G.Selectionsfromnonstrictdifferentiability

Chapter2.Implicitfunctiontheoremsforvariationalproblems
2A.Generalizedequationsandvariationalproblems
2B.Implicitfunctiontheoremsforgeneralizedequations
2C.Ampleparameterizationandparametricrobustness
2D.Semidifferentiablefunctions
2E.Variationalinequalitieswithpolyhedralconvexity
2F.Variationalinequalitieswithmonotonicity
2G.Consequencest'oroptimization

Chapter3.Regularitypropertiesofset-valuedsolutionmappings
3A.Setconvergence
3B.Continuityofset-valuedmappings
3C.Lipschitzcontinuityofsetvaluedmappings
3D.OuterLipschitzcontinuity
3E.Aubinproperty,metricregularityandlinearopenness
3F.Implicitmappingtheoremswithmetricregularity
3G.Strongmetricregularity
3H.Calmnessandmetricsubregularity
3LStrongmetricsubregularity

Chapter4.Regularitypropertiesthroughgeneralizedderivatives
4A.Graphicaldifferentiation
4B.DerivativecrkeriafortheAubinproperty
4C.Characterizationofstrongmetricsubregularity
4D.Applicationstoparameterizedconstraintsystems
4E.Isolatedcalmnessforvariationalinequalities
4F.Single-valuedlocalizationsforvariationalinequalities
4G.Specialnonsmoothinversefunctiontheorems
4H.Resultsutilizingcoderivatives

Chapter5.Regularityininfinitedimensions
5A.Opennessandpositivelyhomogeneousmappings
5B.Mappingswithclosedandconvexgraphs
5C.Sublinearmappings
5D.ThetheoremsofLyusternikandGraves
5E.Metricregularityinmetricspaces
5F.Strongmetricregularityandimplicitfunctiontheorems
5G.TheBartle-Gravestheoremandextensions

Chapter6.Applicationsinnumericalvariationalanalysis
6A.Radiustheoremsandconditioning
6B.Constraintsandfeasibility
6C.Iterativeprocessesforgeneralizedequations
6D.AnimplicitfunctiontheoremforNewton'siteration
6E.Galerkin'smethodforquadraticminimization
6F.Approximationsinoptimalcontrol

References
Notation
Index